Basquette was born in April 19, 1907 as Lena Copeland Baskette, to parents Frank E. Baskette, a drugstore owner, and his wife Gladys Lee (née Rosenberg) Baskette in San Mateo, California. She began dancing as a child. A Victor Talking Machine Company representative saw her dancing to a record in her father's store. He hired her at the age of eight (through her parents) to advertise Victrolas at the 1915 Panama–Pacific International Exposition, held in San Francisco. Basquette later began studying ballet.
