[Sushiglutton]

If he is running well he may not be laggy at all like u say.

I think u should call flop with two OC's and BDSD (ok two flush...) HU.

What makes the turn tricky is that I wouldn't check it if I was villain with any hand. I would always bet the turn, if I decided to CR the flop HU. Correct?

So what does his check means. Here are three suggestions: a) He was bluffing and is now giving up
b) He has a strong hand and wants to go for another CR
c) He has a weak made hand and wants to get to sd cheaply.

a) Makes no sense at all. Why bluff the flop, he will nearly always get called when it's T-high, and then slow down?
b) No reason to believe u are going to bet and there exist no monsters with all those possible draws. Still he may hope u have an A, or intepret his check as weakness.
c) The most likely IMO. I would never do this, but some people get scared if they have a weak hand and an A appear. Checking is usually a scared move. If this is the case he is not folding.

I think this analysis shows that the best line is to check turn and fold river UI.