Villain is a LAG, around 40/30/2,5 I don't have many reads on him.
How do I play this hand OOP? Should I fire second barrel or just c/c turn? The flop is pretty dry, so after he calls me, I don't really know how to proceed on the turn/river.

Poker Room skin
Limit Holdem Ring game
Limit: $0.50/$1
5 players
Converter

Pre-flop: (5 players) Hero is SB with 8 8
2 folds, Button raises, Hero 3-bets, BB folds, Button calls.

Flop: A 4 9 (6SB, 2 players)
Hero bets, Button calls.

Turn: 10 (4BB, 2 players)
Hero bets, Button calls.

River: 10 (6BB, 2 players)
Hero checks, Button bets, Hero ?

You're getting 3-1 on a calldown on the turn with bad RIO, so putting in two bets on the big streets is very bad here unless the guy is a complete ****** always-bet-when-checked-to monkey. Bet/folding the turn follwed by check/folding the river looks fine to me here.

Honestly, check/folding the turn is not that bad. It's probably giving up a little EV because the button's range is wide enough to include some 4x hands and lower pocket pairs, but it's way better than putting 2 BB into the pot if the villain is remotely competent.

It's fine as played, now call his bet, and see how he plays.

Alternative is c/c turn, c/c river.

That sounds extremely weak. It's not all Ax and 9x that call that flop...
4-way, yes, definitely, but HU?

Sorry, I edited my post. Putting another bet into the pot is better than check/folding and betting out the turn is the best way in my opinion. But putting the second bet in on the river is bad because he has to be turning a small pair into a bluff and very few players do that. So unless he is a ****** who bets without thinking (possible at these stakes with those preflop stats), I think calling the river bet as played is bad.

Edit: In fact, check/call is the worst river line. If you think he has enough 4x and smaller pocket pairs in his range, then you may as well just go ahead and bet/fold the river.