Impossible River Value Bet?

[that_pope]

Hello all, this hand happened a few months ago at the 20/40 game at Casino AZ. It was about 3 hours in, and we were at table #2 of the three must moves. I had already lost a big pot to this player when I flopped a nut straight to his middle set that filled up on the river. He is a strong player who isn't in there mixing it up with weak hands, but also someone I don't see bluffing very much.

UTG+1 I raise with JJ, LP1 calls, as does LP2, the villain described above. Everyone else folds except the BB, who also calls.

Flop KJT rainbow. BB checks, I bet, LP1 calls, LP2 raises, BB folds, I threebet, LP1 folds, LP2 calls.

Turn K. I bet, LP1 calls.

River K. I...

Lets get some thoughts before I go through my thinking.