Lucy Arnaz  with daughter Lucie at her first birthday party in 1952

Lucie Désirée Arnaz

Lucie Arnaz had walk-on parts in her mother’s’ CBS television
series The Lucy Show (1962-1968), she had her first acting
role in the series Here’s Lucy on CBS (1968-1974) as Kim
Carter, the daughter of the eponymous Lucy, played by
Arnaz’s real-life mother, Lucille Ball. 

The Arnaz family in 1959 are from left: Lucie Arnaz, Desi Arnaz, Lucille Ball,
and Desi Arnaz Jr.