Is it on BA all the way?
There is a minor personal re-screening in LHR - but your bags will have to be claimed on your first stop in the US so Customs can go through them.
Which airport in NY, JFK?
I think the key here is multi-stop flights. OP, are you taking different flights, or is it that you are on the same flight or carrier and have a simple change of planes? If you are not spending any time in London or New York, and your final destination (without leaving the airport) is LAX, you should clear customs at LAX, not JFK.
Prime example of this. I had a flight from Omaha to Melbourne (VIC) that flew KOMA-KDEN-KLAX-NZAA-YMML. the first OMA-DEN run was domestic, with a change of planes. The DEN-LAX run was also domestic with a change of planes. The LAX-AKL and AKL-MEL run was all the same plane with the stop in Auckland. I had to deplane, but since AKL wasn't my final stop, I didn't clear customs in New Zealand, but did when I got to Melbourne. Same thing on the reverse, and I cleared customs at LAX, but that was also because I had to change to a domestic flight.
If the flight you are on from Heathrow to NYC is the same plane from NYC to LAX, you probably will still be an in-transit passenger at NYC and won't have to worry about customs there. If you are changing to a domestic flight, you'll clear customs at JFK, as you'd have to enter the country to get to your domestic flight.
Without revealing much, could you post the flight number(s) for your trip? That would tell all for what would happen.
BL.