To clarify: the bags will be tagged through if on one ticket/PNR but won't be checked through, they will have to be reclaimed and checked in again LAX at the re-check belt right after immigration.
I did see that the OP was on one ticket/two airlines, I was referring to the One World comments to point out that there are less obvious issues with baggage transfer that can occur also, even if you are on the same airline for two sectors.