Juliette Lewis answers the door of her temporary London apartment. Skinny white jeans, shiny red stilettoed ankle boots, mystic symbol jewellery, no makeup, no face surgery, and a rasping hello. Her West End play is just finishing and she is about to go on tour with her band, she says, by way of explanation for all the mess in the apartment. Shoes and CDs are everywhere. The Police's Greatest Hits is playing; she seems unembarrassed.

Everything about Lewis, the Police CD aside, suggests dark, dangerous, dysfunctional, but then it's hard to work out how much her iconic part in Natural Born Killers is to blame for that perception. People tend not to remember her sweet film What's Eating Gilbert Grape, or the saccharine Evening Star. She says there is a huge difference between who people think she is and what she's really like, but thinks that the two Juliettes might have merged recently. "Right now I'm a complete runaway train of non- conformity," she says. "I like to joke, though, that I get younger as I get older."

Lewis turned 33 in June; it seems slightly surprising that she's still so young, but then she started off in movies early. She was a sullen thumb-sucking teenager opposite De Niro in Cape Fear, and it not only got her an Oscar nomination but also launched her Hollywood career as the perpetually strange girl. She was always on the edge, never the love interest, never quite lovable. "And I had less of a sense of humour and more angst because I was a nonconformist," she says. "When I was 19 I would do photo shoots and say, 'OK I'm ready.' "I wanted to take pictures like Brando and De Niro, black-and-white portraits, no makeup, just me in my jeans ... and they'd have a rack of clothes and a makeup artist and I would be dumbfounded and say, 'Why am I going to paint my face up? This isn't me.' That's unheard of for a female so I'd end up just looking weird, and that shaped whatever public identity I had."

Lewis talks with disarming intensity, which may be something to do with her being a Scientologist. All the Scientologists I've met are a bit like this: they look you in the eyes as if telling the truth is going to save them and you, and they are extremely well-mannered. One wonders what sort of intense epiphany made her chuck in a lucrative, if quirky, Hollywood career and turn rocker. She still intends to do some acting, but it's her music that seems to most interest her now.

"It was a series of stages," she says. "When I was a kid I was always musical and in acting I always used music to prepare for a part. I'd listen to [Pink Floyd's] Shine On You Crazy Diamond and immediately you just feel something, and I'd stretch and connect. For Natural Born Killers I listened to Jimi Hendrix's Voodoo Chile because it's all guitars, imminent danger and brewing chaos."

She knew she could sing nicely and proved it when she sang on the soundtrack for The Other Sister, a film in which she played a girl with autism. Singing nicely, though, wasn't enough for her. "In the last decade I have written songs with various friends of mine and I was always putting off the music thing, even though I knew I needed to express myself that way. I was putting it off out of fear. I had no balls yet. Until the desire became so huge it outweighed the fear. I've done movies for 15 years. There is a security in it ... the trouble is, it was never fulfilling to me. Making movies can be really boring."

She laughs and shrugs: "I have friends that live and breathe their parts but that was not me. It was not stimulating enough."

She decided she had to put a band together in 2003. She called everyone she knew who might know somebody and got the help of Linda Perry, who was once a member of 4 Non Blondes and is now a major-league songwriter-producer. She calls her band Juliette Lewis and the Licks; and the Licks has a treble meaning, she says - licking like a cat, licking like a guitar or licking like a punch. Her band are all pedigree people with extensive experience in other bands: Todd Morse (guitars), Kemble Walters (lead guitars), Jason Womack (bass) and Ed Davies (drums).

Lewis's first album, Like a Bolt of Lightning, was described in the Village Voice as "displaying all the front-bulge bravado of her cock-rock idols" when it first came out in March 2005. The new album, Four on the Floor, is profoundly different: it sounds more mature and more female. Lewis says she drew inspiration for the album from Ariel Levy's book, Female Chauvinist Pigs. "It's about girls who emulate men and think that's empowerment, and they emulate the grossest sides of men," she says. "They get it wrong. So yeah, I have tried to have a strength from nurturing and sensitivity and also have fearlessness but I do have a hostility as well. For instance, all the treatments for the video I got were all sexual and that pissed me off. Does Jack White get a treatment where he's fucking the camera and simulating sex?"

Lewis seems to love the idea of rock life - the tour bus, the pan-European gigs, the living out of a suitcase, the bonding with the boys that will take up the next few months. It is a long, full rock-band tour. It started last week in Berlin, the first UK date is in Brighton tomorrow and she remains in this country until December.

"There's an odd security about having a little travelling home and we all like each other so much," she says. "All of us write on the road and the music is fuelled by love, not partying. Our version of partying is having a couple of drinks. My entire band dances, which is a rarity, and none of us do drugs. I approach the whole thing like an athlete for endurance and stamina. The show is fun for me. That's the celebration. That is the party."

Of course, this wasn't always the case. A decade ago, Lewis liked to party in that other way, the druggie way. By 22 she knew she was so messed up that she checked herself into a clinic. It was a Scientologist-run clinic; this is the religion she grew up with. "Scientology," she says, "keeps me rooted and grounded. I don't know why people have the idea that it's dogmatic. I'm a very questioning person and what's so great about it is that it follows my defiant nature. It's thought-provoking. I find it stimulating and intelligent. It's also practical."

She raves about the clarity of L Ron Hubbard, who founded Scientology, and his books. A couple of them lie on her coffee table, mixed with magazines, arty books, a Pink Floyd CD and an uneaten wrap from a takeaway chain. "Technically it's a religion, but it's more broad-based than that," she says. "It brings in a lot of eastern-style philosophies and it gives you life tools. Simple stuff that deals with communication."

Lewis says her band is like a rugby team. "We're very physical with each other. There's pure enthusiasm and a little bit of innocence but we all work very hard. And, you know, if people say to me is this a hobby ..."

Her mouth thins in rage. She does not want to be put into the same category as other actors turned musicians - Minnie Driver, say. "If you want to start a new career in your 30s as a woman and go for broke, it is at once terrifying and exhilarating. I haven't done a movie this year, I sold my house and I'm hitting the road to tour the record, doing what any other band would do."

Lewis has spent the summer here in Britain in Sam Shepherd's Fool For Love, a play set in a motel on the edge of the Mojave desert. "Eight shows a week sharpens your focus and improves your stamina. This play fitted me. It's high drama. I was born that way. I always had a penchant for it ... When I was younger, though, the drama would bleed over into life and I would get myself into situations that were not healthy. I don't just mean the drugs. I mean when I was much younger I would hang out with tough people. Real hoodlums, gang members, just to see how dangerous it could get. I had a sense of adventure and I put myself in situations that maybe other people wouldn't have ... but I'm alive."

Lewis was born in Woodland Hills, California. Her parents divorced when she was two. Her father, an actor, is now on his fourth marriage. Her mother, an artist, is on her third. They were bohemian, they were clever and they were also Scientologists. When she was 19 she got "emancipated" from her parents. It's often written about in an exaggerated way, she says, with people saying she divorced her parents, when there was no real rift.

"It was because you were more likely to get hired if you were an 'emancipated' minor versus a minor. You could work without restrictions of the child labour laws. It wasn't anything to do with my parents, who were funny, very alive and very supportive. A lot of young actors in Hollywood got emancipated from their parents."

She says now - and this does seem to conflict slightly with her denial of real problems at home - that acting was "the one source of confidence and strength for me. Everything else was a complete disaster. In junior high school, trying to get lunch had more challenges than acting on a TV show.

"Weirdly, I got on well with all the different groups, I was friends with the popular girls. I was friends with the minorities, I was friends with the odd bunch. I just didn't know who I was. I wasn't an outcast in a traditional sense. I'm a dichotomy. In some ways I am very traditional and people don't expect that. For instance, when I was married I loved doing my husband's laundry. I liked it because I liked the tradition of it, because I grew up without it. I grew up where we didn't all sit at the dinner table, we just all sort of got food from the kitchen."

Lewis married professional skateboarder Steve Berra in 1999. The couple were divorced four years later. "He was a workhorse. Everything was work-related and he found it difficult to be in a marriage. We got married during the illusionist period, the grand illusion. We were friends for two years, then we realised we liked each other. We got married straight after we had said, 'Oh my God, I like you,' and, 'Oh my God, I like you too'.

"Then he was off making his first skateboarding film and I was off making a movie. We're best friends now. It's like a family relationship. We always check how we are."

One senses there was some immense pain and disappointment in all this, before it got to the friends bit.

Famously, Lewis went out with Brad Pitt for four years, from the age of 16 to 20. "He's not in my universe at all now," she says. "It seems like a high-school relationship because now he's a very famous person. I look at this person that I shared a bit of history with. I hope he finds happiness because I genuinely loved him. He's a very stand-up, good guy. Four years was an eternity at that time. It was my longest relationship and we both lost our anonymity together. Huge life changes all occurred, all connected to that person. Mmm."

She stares into a blank mid-distance. "We're strangers now. Isn't that weird? I don't know him as an adult, and he doesn't know me. I know that he likes interesting women, always has, and I know that he's a guy from Missouri that grew up in a very small world and it took huge courage for him to leave."

Is there a love in her life now? "Apart from my band?" She laughs again. "You know, I get lonely - I'm not going to lie about that ... I kind of signed up in my mind that I'm giving myself wholeheartedly, full-throttle to my creative life and I don't want to be distracted."

She does see people, though. The last guy she dated, she says, "was a musician as well. We met at a music festival. We've stopped dating now but we're friends." Why did you stop? "He went through that thing where he didn't know how to have a relationship. You know, you either jump in and you try or you don't, and he didn't want to try. He was still struggling and his struggle became depleting." She screws up her face. "I hate dates. It becomes a weird auditioning process. And I've never had normal dating. When you become famous at 19 it does a number in your head, so you find romance in the mundane - isn't it so great that a guy would pick me up at my house and take me to a restaurant?"

On stage these days, Lewis certainly gives it her all: she has appeared on stage in a viking helmet, wearing bikini bottoms. "I think rock'n'roll is extremely sexy and alive, and you have these idiot guys who might project a view on you, like I'm a hot or whatever girl.

"I'm actually very moral and nurturing, but I'm also adventurous. I am challenging. On stage the pixie circus performer you see is not a coy little kitten. I love projecting a female form of strength and vitality ... In fact, I have a friend who calls me Cheetah."

It's a rare thing when someone talks therapy-speak yet still manages to make you warm to them. Juliette Lewis believes in herself at least, so she makes you feel the same. There's nothing cutesy and kittenish about her. She's a proper cat - purring, growling and slinking.

· Four On The Floor is out on Hassle Records.