Doing INTL transfer at any US airports with less than an hour is going to be near impossible. It doesn't matter you are on INTL-INTL (w/ exception NZ in LAX stopover), every passenger needs to clear US custom/immigration. Your flight arrived at TBIA and after custom/immigration, now you have to go to T7/8 and go through TSA. UA Priority line in LAX isn't bad but still long on late afternoon. Just FYI, AC is just as far in T2 just on the other side of the airport.

BTW, just for my future reference, does UA has a transfer desk at TBIA terminal? If not, does that mean you have to haul the checked bags from TBIA to T7 and recheck them?