Perhaps she is Serah's "chaotic" side, and the real Serah is somewhere else or something. After chaos flooded the land, maybe Serah's good and bad personalities split or something, and were reincarnated as two separate people. Who knows.

I find the resemblance to Serah too hard to not find correlation with. If it turns out that Lumina has absolutely no link with Serah at all, I will be very surprised.