A young adult sci-fi trilogy about a cat-like slave species to lizard-like rulers. Cat becomes gladiator, then?

It's three books, the first is red I think, with an illustration of the cat-like female main character. She is a slave/pet of a lizard-like emperor's daughter. She thinks she lives the good life, somehow gets away, and falls into gladiator life where she becomes the best, eventually becoming a revolutionary in the third book (black I believe, with a picture of the lizard-like now-empress) and overthrows the lizards for many animal species.