Hi Alexandra,
Sorry for the delay, I was waiting to here from one of my collegues to confirm the arangements.
It depends on the individual booking with regards to re-checking in at London Heathrow. You will be automatically checked through for all other flights but will have to clear customs in Los Angeles in both directions.
I hope this helps! If I can help you with any other information, please let me know.
Warm wishes,
Cheryl, your editor