According to the Arbiter, it is not actually Lightning, rather a shadow of her. Not truly her, merely a reflection of her power.

Although both her and Amodar talk as though they are real entities. Hmm...

Well, Chapter 2 is too early to do it, it seems. With three maxed layers of the Crystarium, I was able to get Lightning down low enough to bring Amodar into the fight, and he royally creamed me. :P