As Frank Sinatra's granddaughter, AJ Lambert learned early to do things her way. "He bought these bicycles with big wheels at a toy store while we were in Vegas one year, and my sister and I would ride them around the hotel," says Lambert. "It was fun for us, but looking back I don't think the adults appreciated it."

Lambert, 27, the daughter of Nancy Sinatra and her late husband, choreographer Hugh Lambert, also inherited her grandfather's passion for music, if not his choice of styles. Last fall her rock trio Rocket—which is rounded out by drummer Pat Murphy, 36, and guitarist-vocalist Matt Azzarto, 33, Lambert's boyfriend of two years—released its debut album, 7 Miles High, with Lambert on bass and vocals. "I think AJ is wise to not try and copy me or Grandpa," says mom Nancy, 61, who scored a No. 1 hit in 1966 with "These Boots Are Made for Walkin'." "She's her own person."

Raised in L.A. but now living in Sinatra's hometown of Hoboken, N.J., AJ (for Angela Jennifer) never doubted she would join the family business. As a teen she taught herself to play bass and drums and performed with local bands while getting a degree in screenwriting from the University of Southern California. "She likes to carry on family traditions," says her sister Amanda, 25, a painter and freelance photographer. Not that Lambert, who is helping compile a boxed set of her grandfather's movie music, due this spring, thinks he was a closet head-banger. "He wasn't a rock and roll fan at all," she says of Sinatra, who died in 1998 at age 82. "But I hope he'd be proud if he could see me now."