One afternoon in January, Zoe Kravitz was sitting in a sushi restaurant on the second floor of a Los Angeles strip mall, but her thoughts were 3,000 miles and 10 or so years away.

Specifically she was thinking about her weed guy.

He’d come around with product concealed in a guitar case. “He would only talk in code,” Kravitz remembered. “Like, ‘Do you want a guitar lesson today?’ But then sometimes he would screw it up, and be like, ‘Do you want guitar?’ I’m like, This isn’t code anymore.”

She was in her early 20s then, working only on and off, just another smart, young Brooklynite with time on her hands and a propensity for overthinking. She couldn’t have known it, but she was also doing research for her first headlining role, in the Hulu series “High Fidelity,” based on the 1995 lad-lit novel by Nick Hornby. Kravitz plays a Brooklyn record store owner whose life — and love life — is going nowhere particular, a part for which all those guitar lessons were inadvertent research.

“I did a lot of dumb stuff,” she said, but used a more pungent noun than “stuff.”

“Fun stuff,” she said, “but dumb stuff. And was probably a really difficult person to be in a relationship with. But I think maybe any 21, 22, 23-year-old is.”

Back in Los Angeles, the lunch crowd had mostly cleared out while Kravitz talked about living in New York, young and unfettered.

She wrapped her hands around a mug of green tea. She has the names of her younger siblings, LOLA and WOLF, inked across her middle fingers. Certain creepily comprehensive Internet sites suggest that she has at least 55 tattoos in total, many as small as punctuation. She wore a white cardigan. Her hair was cut short and pressed to her scalp in dark waves. Her characters often tend to say less than they know, forever side-eyeing the world around them, but in person she’s sharp, emphatic, easily moved to passionate outbursts by a piece of omakase (“Like butter. Like butter!”) or the two-decade-old “Seinfeld” where George builds a bed under his desk. (“It’s just so funny. Oh, man.”)

It feels like Kravitz, 31, has always been famous — an indelible screen presence and iconic parents will do that — but for years she’s been on the fringes of the action, playing haunted supporting characters in epics like “Mad Max: Fury Road” and the “Divergent” series. But that’s about to change. In a day or two she was leaving for London to start shooting her biggest movie role to date, playing Selina Kyle — better known as Catwoman — in the director Matt Reeves’s “The Batman.” Robert Pattinson plays the Caped Crusader, Colin Farrell is the Penguin, and in true star-of-a-comic-book-adaptation fashion, Kravitz said she couldn’t say much else, except that she never imagined finding herself central to a movie like this one.

“I really thought I was going to do theater and indie films,” she said. “That was what I liked growing up. And also, that was what I thought I was suited for. I didn’t see a lot of people who looked like me in big movies.”

Just a few years ago, Kravitz — whose parents, the actress Lisa Bonet and the rocker/scarf influencer Lenny Kravitz, are both African-American and Jewish — had been discouraged from auditioning for a part in one of Christopher Nolan’s Batman films. Not by Nolan personally, she said. It wasn’t a Catwoman-size part.

“It wasn’t like we were talking to the top of the top in terms of who was casting the thing,” she said, “But they said they weren’t ‘going urban.’ I thought that was really funny.”

A lot has changed since — for Kravitz personally, and in the business as a whole. From Tessa Thompson’s Valkyrie in Marvel’s cinematic universe to Halle Bailey’s Ariel in the forthcoming live-action “Little Mermaid” reboot, it’s become less unusual for actors of color to book roles not originally conceived with an actor of color in mind, particularly in comic-book and fantasy material, where parallel universes collide and anything is possible. (It’s worth noting that women of color have played Catwoman twice before, including Halle Berry in a somewhat infamous 2004 film.)

Sometimes, though, inclusive casting highlights just how much work Hollywood — newly woke but still groggy — has left to do, when it comes to actually telling diverse stories. For two seasons, on HBO’s “Big Little Lies,” Kravitz has played Bonnie Carlson, the yoga-instructor wife of Reese Witherspoon’s character’s hunky ex. Amid a stacked cast of A-listers going for broke — trashing one another verbally, sometimes trashing rooms literally — she’s been an island of wary reserve, her eyes suggesting painful depths.

But in the first season Bonnie seemed to float at the periphery of a story that prioritized the tribulations of its well-to-do white characters instead. In the second season, Bonnie got a real story line — which required her to sit by her comatose mother in a hospital room few of the other characters ever visited. Critics and viewers noticed; the show was roundly criticized for its apparent lack of interest in Bonnie’s inner life.

Kravitz said she’d been drawn to the role of Bonnie — who’s white in the Liane Moriarty novel that inspired the series — because it was a chance to work with the director, Jean-Marc Valleé, and with “this dream cast” of Witherspoon, Nicole Kidman, Laura Dern and Shailene Woodley, who she’d made three “Divergent” movies with and who she’d practically grown up alongside. When she first read the script, Kravitz said, “it felt really fresh and necessary, and like it was filling some kind of creative void I didn’t know I’d really had.”

It didn’t bother her, she said, that the show never acknowledged that Bonnie was the only prominent person of color in the series’ otherwise monochromatic Northern California milieu.

“In the first season, there was something really refreshing about not making that a story line,” she said. “It’s frustrating when people of color can only play a character that’s written as a minority,” she added. “So it’s refreshing when it’s not about that. But it’s complicated, because you don’t want to ignore that fact. Part of our responsibility as storytellers is to tell the truth.”

She said she’d brought up ideas for Bonnie, ways to explore her position in the world of the show that felt truthful. “I pitched things, and it didn’t resonate with everybody and that’s OK,” she said, “It’s not like I didn’t have anything to do. Bonnie has a lot going on besides the fact that she’s a minority, you know? But that detail and that depth would have been delightful.”

Kravitz was born in 1988, when her mother was best known as the Hillman College undergrad Denise Huxtable on the “Cosby Show” spinoff “A Different World” and her father was a struggling musician who still went by Romeo Blue. They split in 1993, when Kravitz was 4; the following year, Bonet and her daughter settled in relative seclusion, on five acres in Topanga Canyon.

Bonet rocketed to fame as Cliff and Clair Huxtable’s second daughter, and then lost that job — she had creative differences with Bill Cosby, beginning when he refused to write Bonet’s pregnancy with Zoe into the series. In an interview, Bonet said the move to the mountains was, at least in part, “a retreat from a world that I was probably unprepared for, at the age I was out there playing in it.”

She also wanted to give her daughter a connection with nature and nurture her imagination. She was a limited-screen-time parent before “screen time” became a topic of widespread parental concern. They had a VCR and a collection of tapes — mostly stuff from Bonet’s childhood. “The Little Rascals.” The original “Freaky Friday,” with Jodie Foster. “Bugsy Malone,” a Prohibition-era gangster musical starring a cast of children. (“That was a big one for me,” Kravitz said.)

Kravitz was always a performer, Bonet said. She remembered the night of her mother’s funeral, when Kravitz favored family members gathered at the Topanga house with a song — “The Girl Is Mine,” by Michael Jackson.

“Zoe put a suit on — I think she had a mustache and glasses — and came out and brought so much joy to the whole room,” Bonet said. “No one told her what to do — it was just pure, from her imagination, with the intention to lift the spirits in the room.”

Kravitz would have been around 9 when this happened. At 11, she relocated to Miami to live with her father, who’d long since shed the Romeo Blue moniker and become one of the biggest rock stars of the age. There are different stories about how Zoe Kravitz’s move to Miami happened, depending on whom you ask.

“There was a whole seduction,” Bonet said, “to a life outside of living in the mountains, with just a monitor and a VCR, compared to screens in every room and private chefs and a big house. There was no real conversation, not between her father and I. But it was necessary. She needed to find out who her father was, and that was the way.”

Lenny Kravitz recalled the situation somewhat differently.

“She wanted to live with me,” he said, “and I wanted to have her. It was time. And as a family, we made the decision together.”

“It really helped me to focus my life,” he said. “I was running around the world touring, man … I had to make some lifestyle changes.”

Still, life with Lenny Kravitz came with no shortage of rock-star perks. He shared a label with the Spice Girls at the time; one year Zoe sat with them at the Grammy Awards. “I don’t remember if it was Scary or Victoria,” Lenny said, “but she was sitting on one of their laps, and she was in heaven.”

But according to Zoe Kravitz, there were more prosaic reasons that life with her father appealed. Lenny Kravitz’s house had Pop-Tarts. Lenny Kravitz had cable. “I just wanted to feel normal,” she said, “and the way my mother was raising me felt very abnormal, even though looking back, it was the coolest.”

Some time after moving to Miami, Zoe Kravitz told her father that she wanted to act. “My mom wanted me to wait until I was an adult to start working,” she said, but her dad felt differently.

“I’m a person who left home at 15,” Lenny Kravitz said. “I would do nothing but support my child in what she wanted to do, absolutely. And it was her decision.”

What everyone seems to be able to agree on is that this would have happened no matter what — that sooner or later Zoe Kravitz would be doing what she’s doing right now.

“I mean, look, she’s a mad artist,” Shailene Woodley said in a phone interview. “Zoe’s constantly looking at the world around her, thinking, ‘How can I leave this place better than it was when I got here? How can I continue to use my talents and gifts as a singer, as a writer, as an actor in a way that’s meaningful and impactful for future generations and have fun doing it?’”

Woodley was calling from London, while preparing for a dinner party. Even as the sound of arriving guests became audible over the phone, she kept on singing her friend’s praises.

“I think — not ‘I think’ — I know one of Zoe’s major superpowers is that she’s funny as hell,” Woodley said, using a different four-letter word. “People don’t realize how funny Zoe Kravitz is. They see her and they see this super-hip, cool girl. But her superpower is humor and comedy and understanding the complexities of life and somehow morphing them in a way that polarizes drama and humor. As a creator I think that’s what gets her ticking.”

Zoe Kravitz is an executive producer of “High Fidelity” as well as its star, and the show — funny and poignant and surprisingly personal — feels like a product of the sensibility that Woodley described. Kravitz, who attended high school in New York and has fond memories of loitering after school in grubby record shops like Kim’s Video and Music, the bygone East Village institution, said she’d long been a fan of the book and particularly of Stephen Frears’ film version from 2000, which starred John Cusack as Rob and Lisa Bonet as a singer with whom he rebounds.

“For some reason,” she said, “‘High Fidelity’ was one of the few pieces of art that my parents had been a part of that I was really able to separate from them. It’s a weird thing, because it can be really uncomfortable and strange watching your mom kiss John Cusack or whatever, but it became a film that I loved and watched and could quote.”

Sarah Kucserka, who developed the Hulu series with Veronica West, said when they brainstormed leads, “the top of the list — pie in the sky, it’s never going to happen — was Zoe.” Kucserka noted, “She has a lot of depth, and that was what this character needed. You couldn’t come at it with someone who only brought one thing to the party.”

Hornby was only dimly aware that a TV version of “High Fidelity” was in the works. But last year, Kravitz asked if they could meet. “She seemed to have a lot invested in it,” Hornby said, “and was restless in her urge to get it as close to what she wanted as she could.” She asked for, and received, his blessing.

“One of the things I’m most proud of about the book,” Hornby said, “is that — I’ve realized this more and more over the years — it’s not just about me. It’s not just about people like me. It’s about way more people than I thought.”

In the initial script, the main character lived in Los Angeles and would have worked at a radio station. Kravitz proposed moving it to New York, and into a dusty basement record shop. Those choices, she said, helped determine other aspects of the show, like setting the story in Crown Heights, a part of Brooklyn where a dusty basement record shop and its owner could realistically survive. (Kravitz, who married the actor Karl Glusman last June, has lived in Williamsburg for more than 10 years, long enough to watch gentrification transform it; her favorite bagel shop is now an Apple Store.)

The staff of the record store now consists of two women of color (Kravitz’s Rob and Da’Vine Joy Randolph of “Dolemite Is My Name”) and a shy, gay man (David Holmes). When Rob runs down her top five heartbreaks in flashback, the list includes women as well as men.

None of this, Kravitz said, was about clearing some imaginary bar for wokeness. They just wanted a cast that looked real.

“I was trying to recreate a world that I know,” Kravitz said, “and that’s what it looks like. It doesn’t look like a bunch of white girls, like the show ‘Girls,’” whose portrayal of New York-area hipsterdom struck many viewers — Kravitz included — as demographically specious.

“If that show was in Iowa or something, fine, but you’re living in Brooklyn,” she said. “There’s people of color everywhere. It’s unavoidable. Same thing with Woody Allen — like, how do you not have black people in your movies? It’s impossible. They’re everywhere. We’re everywhere. I’m sorry, but we’re everywhere.”

Kravitz acknowledged that there might be reflexive resistance to the idea of a gender-flipped “High Fidelity,” as there is to gender-flipped anything, among a certain class of consumers. “I think a lot of white men who identified with the book think it’s theirs,” Kravitz said, “and are ready for us to screw it up, and are going to have trouble seeing it in a different light. But I think if they get past that thing, they’ll see that we actually really did honor the property, I think.”

This kind of conversation is good practice — Kravitz is about to fly to London and shoot a movie in which she plays an iconic comic-book character, and she’s aware that any attachment “High Fidelity” fans may have to an idea of Rob Gordon pales in comparison to the proprietary feelings contemporary nerddom harbors regarding Batman.

“As long as I don’t allow it to get in the way of what I need to do to find this character and make her my own, so that it can be as authentic as possible, I welcome all the fans and their opinions and their love for this world,” she said, with a diplomatic smile.