Not to be a negative Nelly, but I am suspicious of LAX in terms of theft from luggage. I say that having had some items taken out of my wife's bag going YVR-LAX (T4 to T2) - DOH. On this ticket we had a 8 hour layover. Our bags were TSA locked but the theives managed to circumvent the logs (perhaps held TSA keys themselves).
I mention this only as we are headed to the South Pacific as well and there are usually long layovers involved with these flights at LAX before the over water parts to the flights since most leave in the late evening. If you have a dive bag, please take appropriate precautions.
There is reportedly no left luggage at LAX so if you had a long layover, you could potentially claim bags and watch them. It may not be the idea of the best time but it would be better than discovering necessary equipment is missing or stolen.