Normal, Alter, and Lily are all the same person, just different versions. Alter is "corrupted" and Lily is sort of an "alternate reality" version. There's actually very little background out there for Lily since she's just a fighting game character, but the two basic concepts put forth by the creators are that either she's Saber if she hadn't impersonated a man and had ruled openly as a woman, or she's Caster's idealized version of Saber.
Saber/Extra has nothing to do with them aside from being in a "Fate" game and looking a lot like the other Saber. She's cocky and kind of overbearing but relatively likable, with a strong sense of theatre and an exhibitionistic streak a mile wide, and a fondness for drunken, debauched partying.
