The term 'Lucille's Man' refers to the character Desi Arnaz, who was the husband of Lucille Ball and co-star of the classic television show 'I Love Lucy'. Desi Arnaz was a Cuban-American actor, musician, and producer who was best known for his role as Ricky Ricardo on the show. He was also a successful bandleader and businessman, founding the production company Desilu Productions with Lucille Ball.