[Nightwish]

Raise preflop. I say this because you may very well have the best hand and because the LAGs likely know that you're not one of them. They'll cold-call your raise, but they probably won't reraise you preflop and will instead try to push you off your hand on later streets.

The button is almost certainly lying if he told you that he would have checked behind with AA on the turn. He got scared when you bet. If he's indeed a LAG, going for a check-raise would be a good option, but betting out isn't bad either because there's a chance of getting the flush draws to pay 3+ BB for seeing the river.