I'm assuming the AA-operated segments are in J, the BA-operated ones in Y? They will have access to T5 BA J lounges for their outbound connection by virtue of the long-haul J segment and access to the AC in T3 for their return. OW recently changed the rules such that those obtaining lounge access by virtue of travel class may only use their operating carrier's lounge while those with OW status may use any corresponding, accessible OW lounge.