He decapitated her to ensure that she didn't turn into a vampire, yes. He never spoke to her, the entire conversation was purely inside his mind, a figment of his own imagination, as he argued with himself, using her phantom as a proxy for his own inner demons. She says as much, during the conversation.
Thanks to the power of Tivo, I rewatched the ender of the episode in slow-mo, to see what's happening there. It's a very fast jump-cut, but it looks like what Lilah is actually doing is pulling her hand back from a button on the desk that causes the curtains to pull back on their own. Until I hear otherwise, I'm still maintaining that she isn't The First. I'll gladly admit I'm wrong...but I think the "Senior Partners" have her, lock stock and barrel. If they could bring Darla back from the beyond, I think they could handle someone who had willingly given them her soul.
I'm much more curious how they're going to get Angel to working WITH W&H. Really odd, that. Especially given the "If Angel gets renewed comments" from the producers that I've heard. They get the benefit of the doubt from me, though. I thought this season, particluarly the handling of Wes, was going to be extremely lame. I was glad to be wrong.