I sided with Desmond and killed the brain, then after we killed him I was wondering if there was a way to get Desmond's eye glasses, without killing him. And once you leave through the ladder will he still be there when you come back? Because I was thinking of reverse pickpocketing it from him. Also I am on the Xbox 360.

You can reverse pickpocket a fully repaired Metal helmet onto him and he'll remove his eyeglasses.

I have gone back to the lab a couple of times and he's still been there but other people have said he leaves in their games.

He leaves in my game. I tend to off him at the end, for being used ... but you can RPP right then and there.