According to a story he told in his autobiography, he was playing in a club during his early days as a performer when a fight broke out and the club caught fire. He went back into the club when he realized he left his guitar in there. He heard that the fight involved two men fighting over a woman named Lucille. He decided to name his guitar "Lucille" after that, as to remind him, as he said "never to do anything that foolish again." I think he said somewhere else where he's had about 17 or 18 different Lucilles. Some were stolen from him.
Bing! Enlightened. Thanks very much.