Lily Potter's also the name of Lily Luna's grandmother. Lily-the-elder is a very dear friend of mine. I don't really know Lily-the-younger. Not as well as I'd like, at least.
To answer you, yes. Magic in my world's got nothing to do with demons. No one's really certain about what causes a talent for it. It runs in bloodlines, but then it doesn't. It can be inherited, or not. It can appear spontaneously. I suppose it might boil down to genetics, but the wizarding world and concepts like genetics really don't go hand-in-hand.