I have 120 in SB
Villian has 144 in BB

I have A[h] J[h] and raise to 4
Villian smooth calls.

Flop: T[h] 7[s] 8[h]
I lead for $6
Villian calls

Turn: 4[s]
I lead for $10
Villian raises to 30

Whats my play here with FD, Gut Shot, and assume any A is an out.

why do we assume an Ace is a live out?

depending on villain, J9, 65, sets, and 2 pairs are all possible here. in fact with this action at $100NL my detault would be to assume that villain's action represents 2 pair or better.

i think i would check-call the turn if villain is normal, or maybe CR the turn if villain is floaty. as played i would just call and hope to hit an out.

OK.

So if I go for the CR, how much am I raising when he leads for $15?