[sweetjazz]

Make sure you continually update your observations on his strategy, as it's possible he may switch gears on you at some point. But with that said, if you know his strategy, you just have to figure out a counterstrategy to it...

* He's playing aggressive with any two cards. With a hand like J9s, you can either not steal with it or, if you do steal with it, you should have the following postflop plan: bet and 3-bet if you flop a pair (exception: flop comes AQ9, then just call down after being check raised on the flop, betting when checked to); check behind if the flop misses you or you flop a draw; take your free card and fold to the turn bet unimproved (exception: peel once more if you have a big draw, like an OESD and a flush draw, keeping in mind that your J and 9 outs might be good as well). The reason you don't bet the flop is that you don't have any fold equity (assuming your read is correct) and you generally can't showdown J high against a random hand once you have missed on the flop.

*OTOH, be more inclined to steal with Axo (provided you can get heads up with the LAG) and always go to showdown with it. Bet the flop (because you're still a favorite over a random hand even when the flop misses you) and 3-bet his check raise only when you hit the flop or the flop is paired (e.g. KK7) because your equity is higher on a paired board against a random hand.

* Whenever you have a strong made hand (e.g. TPTK), get a lot of bets in. Don't keep raising if the LAG's range is no longer a random hand, but I'd generally cap the flop and bet out from there with this kind of hand, calling down when raised. If you see the LAG is still being a monkey with turn raises after flops get capped, you can adjust but most people don't hate money that much.

* Accept that his strategy is very high variance and he will take money from you when he runs good. Your strategy is still better in the long term and you will clean him out given enough time.

* Finally, go back to the first sentence of this post. Often, in these situations you will hit a good run where you take a lot of money off the LAG. Pay careful attention to see if he shifts gears. If he's no longer checkraising flops with any 2, you have to adjust again. Hands that you might have 3-bet on the flop before might be called or folded given your opponent's change in strategy. When he stops check raising with his complete misses, then you shouldn't be paying off with your weaker hands anymore.

Reread the last chapter in Theory of Poker where Sklansky discusses ways to exploit opponents' tendancies.