If you remember my analysis on Lucifer, there are a couple of things I forgot to mention the last time.
Lucifer appears to be the perfect example to represent the figurative and literal meanings of the words "fat cat." Now of course, this suits him in the literal sense because he is a cat that is physically fat. Due to his excessive eating, laziness, and unwillingness to get exercise over the years, Lucifer is extremely obese. Now regarding the figurative term, a fat cat is a rich, greedy person who, due to ownership of large amounts of capital, is able to "live easy" off the work of others. Lucifer fits this well because his mistress is a wealthy woman who treats him like royalty, and Cinderella is forced to do everything for him, making him live "the easy life."
With animals that are kept as pets, dogs and cats often seem to be natural enemies. Dogs are generally portrayed as loyal and friendly, while cats tend to be sneaky and cunning. This is illustrated in Cinderella, in that the villain (Lady Tremaine) owns Lucifer, the evil pet, while the protagonist (Cinderella) owns Bruno, the good pet. Much like the relationships Cinderella shares with the Tremaines, Lucifer and Bruno strongly hate each other, and they fight like cats and dogs, literally speaking. ;) Also, Bruno is a friend to the mice while Lucifer always attempts to eat them. Lucifer, like the Tremaines, is very manipulative, devious, and always attempts to get both Cinderella and Bruno into trouble, taking great pleasure when he seems to have achieved it. In fact, it is very possible, even though it is not explicitly stated, that since Lady Tremaine did not know that Jaq and Gus stole the key to Cinderella's room, Lucifer wanted to help her keep Cinderella locked up when he traps Gus (who has the key) under the bowl. Then Bruno gets his revenge when he is summoned to the tower and scares Lucifer so much that the cat falls out of the window. After that villain's defeat, Cinderella then defeats the Tremaines by revealing she has the matching slipper.
Besides his name and fur color, Lucifer's mean nature is also symbolized by his sharp claws, which are always displayed throughout the movie. By doing so, he is always ready to strike at the mice when they come his way. Lastly, without counting the sequels, it can be argued that Lucifer survived his fall because of the popular myth that cats have "nine lives." Another theory is that cats have an ability to fall from extreme heights and land standing without injury, due to specialized muscular reflexes.