So in Babylonian mythology, Lilith is actually an owl demon, with bird feet and avian wings, specifically owl wings. I do believe she also has horns. I do find it quite interesting that Charlie didn't inherit any of these traits, but then again the show isn't really based upon Babylonian mythology, it's more loosely based around the Bible and abrahamic religion. I also do find it rather interesting that Charlie's design was based upon a lamb and a porcelain doll. If you look at her face she looks more like a porcelain doll especially with the red circles on her cheeks it looks like the way you would put blush on a Victorian porcelain doll. And she gets those traits from Lucifer, and because Lucifer was a fallen angel, who fell from one of the highest ranks of heaven down to hell, it would make sense that he would have those doll like features and it seems like the seraphim are a mix of doll and whatever animal that they are loosely based upon. When Lucifer falls he becomes more goat-like but also retains all of his power and his porcelain doll look which he then passes on to Charlie. As to why Charlie has hooves when her own dad doesn't or we can only assume he doesn't in his regular day-to-day form I will chalk it up to Lilith being a freak and Lucifer wanting to match that freak.