Villain is unknown, sat down about 20 minutes before this hand came up, no history with Hero. Hero has been relatively active and also getting good cards but Villain probably doesn't know this.

UTG straddles to 10
folds around to CO
LAG ($420 stack) in CO raises to 40
Villain ($967 stack) calls on the button, SB folds
Hero ($1.7k stack) in BB re-raies to 165, UTG folds, LAG folds, Villain tanks for about a minute, double checks his cards and then goes all in for $802 more.

What should be the correct calling range for Hero in this spot?

This actually isn't that deep (less than 100 BB effective, with the straddle).

You need 40% equity, so we need to estimate a range for V and then figure out what cards have at least 40% equity against that range.

In a vacuum, I'd suggest starting with QQ+, AKs but discounting QQ by 50% to reflect that it's less likely that V will shove 100BB with that.

Against that range, you should call with KK+ (KK has 45% equity). AKs has slightly negative EV (35% equity).

But all of this is highly sensitive to V's shoving range. You can have as many answers as you're willing to have ranges.

It turns out that discounting QQ doesn't matter. Even if you put all combos in, it's still KK (though AKs gets even closer at 38%).

If you put all AK in his range, AKs makes the grade. QQ is epsilon below breakeven.

In the real world, I'd call with KK and fold everything else until I had a better read.

Time for the OP to download an equity calculator. There are free ones, although the ones you pay for have advantages.

You need about 45% equity. You need to simply calculate the range your hand has that equity to see what you call with.

KK: Fold if his range is tighter than KK+, AK
QQ: Fold if his range is tighter than JJ+, AK
JJ: Fold if his range is tighter than TT+, AQ+
AK: Fold if his range is tighter than 99+, AQs, AK

If you can't put the villain on a range he'd do this with, fold.

so the fact that Villain flat called the original raise and then 4-bet the squeeze does not skew his range? I was mostly curious about that.

Does he have any reason to have a read on the LAG yet? That would really go a long way towards ranging him. If he knows the LAG is a LAG, I would put more strong hands in his range.

Villain had only been on the table for a little while, but LAG was involved in a lot of pots so Villain must have noticed.

What's your hand?

I intentionally left my hand out and framed it as a calling range question, but obviously our hand matters because it makes certain other hands more/less likely in Villain's range.

My hand was AQo, if you are interested.

Opponent's ranges aside, that's a fold in a vacuum. You should have at QQ+ to continue. You said it yourself, villain is unknown. Against unknowns this is a clear fold that shouldn't be given a second thought.

You were probably considering your image and the credibility of your 3-bets, which is why you were thinking about calling. Amirite?

In that case I would add this to what I said before.

You are almost certainly behind. Villain is asking you to call 802 to win 1174 minus rake, so you are getting less than 1.5:1. If Villain always has a pair smaller than queens, you have the equity to call this; however, if we give him a range of JJ-88 and AK, now you no longer do. That is how precarious a call would be here. In fact you could even expand his range of pairs down to 66, but as long as there's a chance you'll see AK, you can't call profitably getting 1.5:1, and here you're getting less.

That is a BEST-case scenario where Villain has a capped range. In practice, I have seen people play KK like this too, and I'm sure those kinds of Villains have AA in their range here as well. I think you can safely fold AQ.

I know that doesn't answer your question of what your calling range should actually be...but I think we can at least say it should not include the hand you actually had.

The squeeze is a nice play here but I think it's very easy to let go when villain wants to play for stacks.

Also, I would likely 3! a bit less to make folding cheaper specifically in case he comes over the top.