Complex sentence: Dianne at the time was a part of a dance act with her cousin Liz, who was talking about dance on her own, so Lennie asked Diane if she was interested in an act with him.
Split into simpler sentences: Dianne at the time was part of a dance act with her cousin "Liz". Liz was talking about dancing on her own, so Lennie asked Diane if she was interested in forming an act with him.