Lucille Ball is the name of Aunt Prue's Siamese cat. She was named after the actress because the Sisters love "I Love Lucy!", a television series.
In Beautiful Creatures, she is introduced when Ethan goes to visit his great aunts, known as the Sisters. Lucille was not let out of the house, except for exercising. Aunt Mercy would put a collar and a leash on Lucille and attach to a clothes line in the yard. Then Lucille would be able to walk the length of the yard.
In Beautiful Darkness, we learn that Lucille is a Caster cat. She was given to Aunt Prue by Arelia to help her find her way around the Tunnels. She has a supernatural connection with Ethan, allowing him to foresee what's the next place to go by Lucille allowing Ethan to access her vision.