I thought that the Arrivals Lounge access rules had been tightened up after AA had moved back to T3. aa.com says with regard to the AA Arrivals Lounge:
Access
Flying on American Airlines?
You can enter the Arrivals Lounge if you flew on American to LHR on a same-day flight and are*:
- Flying in Flagship® First, Flagship® Business Plus or Flagship® Business
- AAdvantage Executive Platinum® or AAdvantage Platinum Pro®
- ConciergeKey®
- oneworld® Emerald℠
- British Airways Premier
Flying on British Airways?
You can enter the Arrivals Lounge if you flew on British Airways to LHR on a same-day, long-haul international flight arriving in Terminal 3 and are**:
- Flying in First or Business Class
- oneworld® Emerald℠
- British Airways Premier
https://www.aa.com/i18n/travel-info/...als-lounge.jsp
Arriving on a BA flight to T5 no longer provides access to the AA Arrivals Lounge. I seem to recall that there were reports that the BA Arrivals Lounge had a similar restriction for AA flights arriving in T3.