The other problem is how does OP get into the lounge without an invitation / BP? The *A Lounge is very busy that time of the day and I am not sure how the dragon will handle it.
I would:
1 - Call the airport office at +1-310-646-9813 to find out how to do this
2 - See if they can at least add the inbound and outbound AA flights to the BR PNR as Information Only segments so they know where you are in case things go wrong