Live tournament with 12 players remaining and 10 make the money. I am currently chip leader. Villain is LAG type player who seems to be pretty splashy. I have 31 BB and Villain has 29.5 BB.

Blinds: 2000/4000, 500 ante

Villain (Button) limps on the button.
Hero completes from the small blind with 105
BB checks.

Flop (pot: 16500, 3 players): 467
Hero checks, BB checks, Button bets 11500, Hero ?

This seems to be a spot where ICM indicates I should just fold this close to the bubble since there are a lot of short stacks at the table and with Villain being the only other deep stack, but my hand seems to have too much equity against his range to fold from a chip EV perspective. If I fold here, I'm probably being too exploitable and don't have enough semi-bluff hands in my calling/raising range. If I call, I'm left in a tough spot on the turn if I miss and he barrels. Raising seems reasonable but I'm curious hear any suggestions/thoughts.

In order to calculate this, you would need the exact stacks of all players involved, the payout distribution of the tourney and details on villain (and to go a step further also info on other villains would be helpful, es. if the shorter stacks are aware how to play the bubble adequately).

Without further info: Call and evaluate turn, this is way too good to fold and whether raising is good depends on the required info above. U can probably call off a lot of non-ai barrels when hitting draws, if villain is aware that he should bluff wider than usual in the spot.
Remind that villain also faces risk of elimination as u're nearly equal in stacks, so if he is aware of how bad it is to bust now, there is a significant "first mover advantage". From my experience players tend to underestimate ICM influence on average (idk about live play, but since ppl are significantly weaker live than online for the same Buy-In, I assume it's at least as bad there, BUT: this might be wrong, cause railing the live tourney probably feels worse than just opening another one online), so c/r jamming or sth might just make him call A7 etc., often better to be on the safe side and flat.

So yeah, posted this on the wrong forum since this was a live MTT. Sorry guys. Anyway, there were two tables playing 6-handed and the other stacks during that hand were:

BB: 12BB
UTG: 8BB
MP: 15 BB
CO: 15 BB

Don't have too much information on the Villain as I'd just gotten moved to this table sitting to his left. The first two hands, he opened and picked up the blinds and antes. This was the third hand. The rest of the table seems to be in 'survivor' mode, folding all but the top 1% of hands.

Ultimately, I decided on a check-raise to 55k, BB folds, and Villain calls.
In retrospect, I hate this sizing because it leaves me committed on brick turns since I only have ~45k behind and the pot is now 126.5k. So yeah maybe flatting is best since he probably isn't folding his 7x.

Turn: 6

Hero checks, Villain jams for ~39k.

A few of the hands in his flatting range have improved (sets, 56s, 67s etc.) but this player is definitely capable of taking this line with two random cards. Am I committed to calling off this turn or should I check/fold with ICM considerations? I would only have ~10BB if I decide to fold here.

You can't fold to the flop bet with so many chips behind. Obviously ICM implications but you can happily call with all the outs in the world and see what happens. Not thrilled to x/r since getting a chiplead stack all in so close to the bubble on a likely coinflip is too reckless.

I think we have to x/f turn I don't expect villain to fold 7x since most of the 7s he limped btn with will have some connectedness like 75s or 87s rather than Q7o.

Even with 10 BB behind with how nitty the rest of the table has been you should get some good spots to jam btn/sb if villain ever happens to fold a hand.

For me you do one of 2 extremes. You either play conservative, call flop and check/fold that exact turn. Or, you put decision to villain for all his chips. Online, I probably shove as most are icm aware. Live, this doesn't seem to be the case, so I would play conservative.