CAUTION!
You will have major problems if you miss the LAX-PPT flight. There are only a few a week, so there may be a wait for the next one of a day or two if you miss it, or all the seats are booked for the next week! (OK, on Tuesdays, I think, there are two LAX flights).
Second, if you are going business or premium economy, there may only be Economy seats left - and there's no EU261 protection. French Polynesia is in one of the three French overseas territories that vote for a representative in the EU parliament - but the only one not regarded as part of the EU!
So allow a day in LA, or at least get the first flight out of LHR. The advantage of LHR-LAX is that there are many alternatives, which should get you there before the 23:55 overnight - but chaos with weather anywhere, and you are stuffed.
ps. I was booked NRT-PPT in Business and ATN have cancelled the flights until end of October next year. But they refuse to rebook me in Business Class from LAX, saying that since my flight was a reward flight I need award spaces! That gives you an idea of how they handle problems.