switchbladeeyes

But why "save" Nick from thinking he's possessed by a demon?

Nick behaving like a vampire is exactly what LC wants. If Nick wants to chalk it up to being possessed by a demon, it seems like it should be a big "so what" from LC's perspective. If going to an exorcism is gonna shift Nick's mindset and knock him off the vampire trajectory, why would LC do that?

For me, the moment when LC decides to give into Nick's demands to take him to the exorcist is one of the most unexpected things I've seen from him on the show.

I wonder if LC even knows why he did it.

I do think that once he's at the exorcism, he becomes convinced. At which point, he believed he was trying to save Nick from an actual demon.

But why take him in the first place?

You could be right though and LC was trying to save Nick from the belief in a demon. In the Raven, he can see that Nick is greatly distressed, and while that may not have much of a motive for him to help Nick in the past, we're at the part of the show where we see their relationship changing quite a bit. It's not the only moment that LC undercuts his own agenda for Nick's benefit (covering for him in the immediately preceding episode, NiQ, being another such moment).

The show always keeping us on our toes and guessing!