When HAM had a BA lounge it was a small lounge with just one person maintaining the desk and rarely more than a few passengers in there. The lounge was only used for a few BA and DBA flights to the UK, as well as a few Iberia flights to BCN and MAD. I've never seen the lounge full or even anything close to its capacity.
That makes it easier to let one in if one asks nicely and would have qualified after the flight. It's not a right or even the rule, though.
Today it wouldn't work in HAM, as the lounge is now a third-party lounge.