Or CX and/or BA policy, who knows, but I have never heard of such a thing with AA.

As mentioned above, AA lounge access policies have a minimum age for entry w/o an adult. This is no different than the policies that require you to have a certain status, class of service, or qualifying itinerary for entry to the lounges. They certainly don't hand out vouchers to every AA EXP who tries to access a FL without a qualifying itinerary, so similarly I wouldn't expect a voucher for being underage.