im not sure if they will let you in but try and use the flag ship lounge in ord before your aa ord lax flight
when you land in lax go to the lounge in T4 the aa lounge is much better than the cx lounge in the international terminal. sad but true

even if you have to check in again at the cx counter for cx boarding passes dont worry, the cx F line should be very short.

enjoy the flight and let us all know how it went