There is a plethora of airline lounges at T3. Turkish Airlines may share another airline's lounge, or they may have contracted it to Servisair. I assume that the AA arrivals lounge is landside, so she can ask the TK check-in staff when she's ready for the next step. Being landside at that point just keeps her options open. At worst, you can pay to get in to the Servisair lounge, in case she's airside and the lounge that TK uses is different and turns out to be a real hell hole.