If the turn pot is $1,858 and you only having around a $1,000 left, then I can't see how you can fold heads up had the LJ bet the turn. Therefore, since you are not folding, I am betting the turn hoping to get the LJ to fold any of his better flush draws that would beat me on the river.
Is LJ going to fold a worse flush here after calling off so much already? I don't see it. But you certainly can get him to pay off chasing here especially since he's going to be reluctant to bluff river.
Ahxhxx has 23% equity on you (he might overvalue this, given you have 2 hearts, his odds are much worse). He's getting 1000 to win 3000, so he has slightly worse than correct odds to call, but thinks he will have correct odds.
If LJ has worse straight, he's folding to your bet. He *might* spazz shove river if you check.
If LJ boated, he's calling anyway and you are getting stacked on the river, so no point in discussing this part, unless you are considering folding the river. Given that your hand is very telegraphed what it is, he may think he can bluff you off of it. Given his bluff river hands are pretty much the same hands you call on the turn, I don't see that trying to induce a bluff is worthwhile of a plan.
SB raised pre, then bet folds, does he have AA with Ah? Unclear what that guy is even doing.
Houston Live 1/3 game, I shove the turn, expect to be called with a nut flush draw, with 9T without hearts, and boats.
This call, call line is usually a good draw, not the nut straight, and you block fd so that leaves boat draw more likely (you unblock top and middle sets). He is tight passive so I don't see him trying to get you off a chop otr. I would check back and fold if he donk jams otr.