Lucie Desiree Arnaz was born in 1951, just nine months before her parents, redheaded B-movie actress Lucille Ball and Cuban bandleader Desi Arnaz, changed television history with the premiere of I Love Lucy. Twelve years later, Lucie finally made her own official TV debut on The Lucy Show, having spent a decade watching younger brother Desi Jr. get most of the audience exposure. In 1968 Mama Ball signed both kids as regulars on her third series, Here's Lucy, the dream coming true that her offspring, born in a trunk, would really live out of it for the rest of their lives. When Desi dropped out to try his hand at movies (a bid that failed), Mother and Daughter held the TV show together. Then early this spring Lucille announced she was giving up the weekly series. A deciding factor, according to one rumor, was her daughter's desire to pull out as Desi Jr. did and try to make her own marquee name. And right now, Lucie, at 23, is doing just that.

She is with the first national company of the Broadway musical Seesaw as Gittel Mosca, the hapless Jewish dancer from the Bronx who falls in love with a married square from Omaha—thus taking over a role played in earlier incarnations, both musical and dramatic, by such luminaries as Anne Bancroft, Shirley MacLaine and Michele Lee. "This is my Hamlet," Lucie figured, and the critics at her premiere in Boston all went happily through the hoop. Variety proclaimed: "She steps into stardom on her own terms...bowling over an audience unprepared for such a surprise package of talent and assurance."

Lucy Sr. and her mother, Lucie's grandmother, came to see the play during the first two weeks. To avoid causing a distraction, Lucy did not enter the lobby until the lights were dimming. At intermission she hurried into the theater manager's office and asked intensely: "Is my daughter as good as that in the second act?" and then crumbled into tears.

Long-legged like her mom, but with the dark coloring of her father, Lucie looks back fondly on her mother-supervised apprenticeship. "Please don't leave us [Desi Jr. and herself] on the show to be made fools of if we aren't any good," young Lucie says she begged. "I wanted to learn very much. I asked more than she told ..."

Mother still keeps a bedroom in her Beverly Hills home for Lucie, though she moved away at 18 into her own Century City apartment and now has a small and much-loved two-story mock-Tudor house in Westwood. She constantly shows off a wallet-sized snapshot of it while on the road, almost as if it were a child. Her marriage at age 20 to little-known independent producer and director Phil Vandervort ended discreetly after a year. "It was my fault," explains Lucie. "I got married too young. I still do love him and it could very well work out again." The closest she has come to gossip-column notoriety was her friendship with female impersonator Jim Bailey. He was anathema to her mom—particularly when Lucie and Desi Jr., at the time living with Liza Minnelli, would all show up at a nightclub to watch Bailey impersonate Liza's mother Judy Garland. "Both of us were hurt a lot by things people said," Lucie confesses, adding, "Jim Bailey was a good friend in those black days after my marriage broke up when I really needed a friend."

Seemingly now settled down, Lucie casts a bemused eye on Hollywood. "I don't believe a lot of it. I go along with it up to a point, but I try not to get tainted by it. I gave a party for Bette Midler. That was the first big Hollywood party I ever went to," she laughs, "and it was mine." Right now Lucie is submerged totally in her work and, if her perfectly possible dreams materialize, will in ten years be "putting pictures in my scrapbook of my hit Broadway musical, sending my two children off to nursery school, feeding the dogs and rushing to get to the studio." Just like mother.