I suspect that the AA landside checkin desks will not accept a bag for the next day. So don't take your bag into the landside public area.
The AA bag recheck by the customs exit (before you are in the public landside area) may accept the bag, but may not. If you want to try, make sure the bag is tagged to OGG when you check in at LHR. AA may not do that because they have a shorter (typically 12 hour but can be less) restriction on the length of a connection for which they will hold bags in the airport.
So in summary you have to:
- Get your bag checked to OGG in LHR.
- Get the AA recheck in LAX to accept your bag the day before. They may not check too carefully...