Preflop and flop seem standard. I could see checking behind on this flop as well, as almost all pocket pairs will continue, and they're ahead of you at that point.
Your turn bet is only a little more than 1/2 the pot. Had villain seen you play your counterfeit hand? Were you value betting that hand bigger than 1/2 pot? And when villain showed his bluff, was he bluffing someone who bet half the pot? How big was his bluff in relation to the pot/bet?
His check raise is not very big. It looks a lot like a semi-bluff check raise that thinks it might have fold equity against two big cards that still didn't pair up, while also building the pot a little bit if the flush card hits.
Personally, I think I make a bigger turn bet ($75-90), but that may just be preference.
Once check raised, I think your plan of flatting and calling most rivers is fine too.
The K
though (and really, any club) are some of the rivers I think that you shouldn't call. Two clubs would have matched up perfectly with this pattern. Suited clubs (any combo) may have limp called pre. And the LAG may have floated you OTF, just to set this up in case the turn was a club (and he would have otherwise shut down if no clubs came). I wouldn't be surprised to see him flip over the 4
5
here. Fits the way he played this hand perfectly.
Without better reads on this guy (does he think you are competent enough to fold this? How bluffy is he (other than the one hand)? In what other ways is he "competent"? How do you know he is level 2/3?), or any additional history, I'd just fold for now and move on. But then again, I may be nittier than most.