updated 06/25/2009 AT 1:35 PM ET
•originally published 06/28/2009 AT 7:50 AM ET
Twenty years ago Lenny Kravitz released his first big international hit, Let Love Rule. Around the same time, his daughter Zoë came into the world. Now she’s following her famous dad into the world of rock ‘n’ roll with her band Elevator Fight.
“She’s loving doing this music,” Lenny Kravitz tells PEOPLE while promoting his latest tour to mark the 20th anniversary re-release of the record in London. “It’s a trip to watch.”
In terms of advice about the rock world, dad keeps it to himself. “I have nothing to do with it, which is brilliant,” he says. “She is just doing her thing, and it’s really good. And everyone’s chasing them to sign them.”
Kravitz, 45, is completely supportive of his daughter, whose mom is actress Lisa Bonet, 41 – despite the shaky world of the music business. “Whatever she wants to do, I trust her fully,” he says smiling. “She’s got great instincts. She’s much smarter than I am.”
His daughter, who will turn 21 in December, has varied strings to her bow, in any case. “She has other things which is good. She’s done six or seven films now,” he adds.
Nothing to Prove
Sitting under a tree in a leafy garden just off the swanky shopping haven of Sloane Street, he considers that in the last two decades he has become more secure in himself. “It sounds clichéd but it’s true. I don’t feel I have anything to prove. I just feel like being creative. And I actually feel better than I did 20 years ago – physically and mentally.
“I’ve done that 20 and now I’m going to do this next 20, God willing, and end up being Mick Jagger.”
The film has led to some new avenues that he’s exploring. Precious director Lee Daniels “wants me to be the lead in his next film,” says Kravitz, “and I’m getting all these other scripts. I’ve just been reading and reading over the last couple of weeks.”
As for the future, “I’d like to do something at the end of the year or early 2010 and get a film in the can,” he says.