I’ve visited the BA lounge twice within the past year when connecting off of the BA67 and onto an AA service. I received access to the BA lounge both times. For whatever reason, they needed to see my gold card as the AA boarding pass wasn’t sufficient to feed into their system. One of the times, they even apologized that they wouldn’t be able to give me access to pre-flight dining as my onward flight was with AA. (I didn’t expect it anyway.)

Unless the BA lounge is crowded, I find it superior to the AA lounges, but I recognize opinions may differ.

There are long-standing reports (both here and on the AA forum, I believe) that BA denies access when they are, or expect to be, full. I’ve never personally been denied access. The closest I came was (several years ago, as an AA OWS flying AA to MAD) having the nice lady at the front desk say she “almost” was going to turn me away because they expected to be full. I promised to be respectful and leave if they did become full. She gave me access and I did leave when it filled up.