You are connecting to a US domestic flight.
This means you must clear immigration and customs at LAX.

Even if you had a short connection, you have to clear immigration, collect your bags and clear customs with your bags.

For connections, you then have to go to a connections counter to hand your bags back in.

This is a OW connection, so BA can inter-line the bags as the connection is within 24 hours, albeit next day. All it had to do is to issue the tags. The issue is whether the AA transfer counter will take your bags as you not BA have to manually check-in the bags again at LAX.

You will have the same issue if you were flying AA all the way. You might be better off asking on the AA board for this.

The issue here is whether you want to. You will already have to collect your bags. Do you want to hand your bags straight back overnight at LAX or just take the bags to the hotel with you overnight.

For my peace of mind and safety of the bags, I would rather keep the bags with me but this is your call.