Absolutely! ^

Sometimes it is easier for us to use a FastPass, use the AL and use HEX or walk to our departure terminal, then use the departure terminal's lounge to wait. There ALWAYS seem to be showers available at the AA AL, for one thing, and it is invariably less crowded than the BA F lounges in the mornings (finding two seats can be challenging sometimes!)

Folks just need to remember the LHR AA Arrivals Lounge closes very prmomptly at 14:00 / 2:00 PM, or perhaps minutes before - meaning they may be passively trying to prevent anyone arriving on AA 136 from attempting to use the lounge.