If you have LAX-SFO on AA (irrespective of class) and SFO-DOH (QR J) on the same day, and assuming all lounges are open by the time you travel, you will have access to the AA Flagship lounge and any of the Admirals Clubs before your LAX-SFO flight, even if the 2 tickets are booked separately. Theoretically, you should also have access to the oneworld LAX lounge and the AS lounge, although I'm not sure if in reality lounge receptionists are well informed to let you enter given they are in different terminals. You should however note that, if these tickets are bought separately and in different PNRs, you will not have free bags for your LAX-SFO flight (if booked in Y), the bags will not be through-checked, and you will not be protected in case of misconnection.