This one is tricky.
BA website states that lounge access will be granted on fully flexible domestic fare (which is only 'J' or 'Y').

However, we all know that BA shorthaul/domestic flights book into 'J' when purchasing a longhaul J or F ticket. This is true for BA fares. If you want to buy an AA fare it will book into 'I', 'C', 'D' or 'J', depending on the booking class on the transatlantic segment. So, if one purchases a discounted business class EDI-(BA)LHR-(AA)JFK ticket BA will not really treat anything but 'J' as business class? Lounge access will be granted because the passenger is continuing on a longhaul J, but what about TPs/miles?
When buying such a ticket on AA.com the booking page clearly states 'business" for both 'I' and 'D'.