[carrotsnake]

Buncha key points that you should answer to yourself -

1) When lags play this way, something you might notice is they minraise some hands and not others, what kind of raiser is he ? Does he always minraise, or does he vary it. If he varies it, an ace or big hand seems far less likely.
(For what its worth, preflop is pretty bad, repop to around 11 or 12, you've got a semi-fish, work with it).
2) Whats he do with different hands on the flop. If he has AQ, does he raise here. a LOT of LAGs would, but do you think he actually realizes your running cold or are you just assuming this or is he braindead ? Would he raise with KT ? I'd hope he raises KT(not like its very likely with you with 2 K's) The other thing is does he float at all. This is where aggresion postflop is key. If he's aggro, he's more likely to raise or float. If he's more passive, he'll just call and will fold most trully bad hands.

3) All that said, whats next ... And its interesting, and you have plenty of choices. Again, it'll depend on the fist 2 questions. I'm gonna go with my read of a 60/30 which is moronic and bluffy in general, but perhaps with a touch of intelligence in there somehwere to know how to float and scare you. With all that in mind, if you bet, he's not calling with pretty much any worse hands, he's shoving some worse hands(T9 perhaps, as well as some others) and shoving/calling all better. So betting seems pretty mehhhhh. Check then. After that, bet size matters a lil, but to be perfectly honest, if he bets a normal amount, I'd shove. For one, I probably have 6 outs at the worst. Two, he's laggish, its easy he could have some semi-bluff hand(QK comes to mind, as does TJ). Three, you very well could fold out QJ if he's a folding kind of person(some people like to do it, I swear, no idea why). And lastly, you do have Kings against a guy whose play is probably quite erratic, and while the board is pretty meh, its VERY hard to put him on any true ace. AQ usually raises flop. AJ sometimes does, and if not, so be it. QJ probably raises flop. The problem with calling is it leaves you in a pickle on a lot of rivers. Now, it may very well be better, and I wouldn't have a problem with it, so long as you can trust him on the river, but again, going with a steoryptical read of a LAG like that, you can't and he could potentially make you fold the winner in a very big pot, which is bad.

So probably your options are something like
C/C(with good river ideas and reads) > C/R > C/f >>>> B/anything