Hmmmm...
The set assessment seems completely accurate (I missed that one in my last response), but I still like betting out.
First of all, LAG is very likely to have KQ, but may also have been betting JJ or QQ, something like that, in which case, you just take it down by betting out (and indeed win more with the checkraise).
But there are more KQ hands than JJ and QQ together, so I'd rather have him flat call the flop and turn with KQ or even KJ maybe. Anyhow, on the KQ/KJ scenario you win something like $140 from LAG (12 instances of each). You win $27 if he has QQ/JJ (6 instances of each). And you lose $27 if he turns over AA (certainly more against KK, but that's rare), which I assume he raises (surely he's not raising KQ against your bet).
But that assumes that everyone else has missed, which obviously isn't the case. Worst case scenario is that both LP players are drawing to a set, which certainly isn't necessarily the case. But, if so, one of them hits about once in 4. So, you basically take the place of LAG here against the set. If LAG flat calls you, then one of the LP players, I think you're in major trouble and can then quit (or so I'd like to think here. I'd at least like to give up my AK to 2 flop callers on a serious bet). So, you lose an extra $27 once in 4 times on the worst-case scenario of having both LP callers drawing to the set (or having 2 pair with 86s, which from the perspective of AK amounts to pretty much the same thing).
That's my pitch for betting out, anyway. I don't see how the checkraise accomplishes more, but would love to hear a more detailed argument for it...
