I haven't made that connection before (usually it's AA to Air New Zealand), but you do have to change terminals, which when I was at LAX, you had to leave a secured area, walk around the airport & then clear security again. (if the situation at LAX has changed, please advise) Before I found the correct terminal, I wandered into one & just about died when I saw the security line.

LAX is shaped like a horseshoe, but it's not easy to just "cut across" to the other side. When you get to your new terminal, you would then have to stand in line to re-check your bag, then stand in a long security line again. Is your layover long enough to justify doing this?

DG