I would rather have a different type of skin rather than the Carbuncle alltogether. (Which to me fits more with a SMN) I would love to have a more masculine option for a pet. Maybe a Mammet or some sort of Magitek bit. Lily is an artificial being after all, an aether construct made to supply healing. Mammets and magiteks are essentially the same thing, artificial constructs too so it would not be too strange to see them act as SCH pets.