I flew to JFK from T5 in August and arrived about 4 hours before departure. I was flying Club and wanted to use the lounge. The check-in dragon informed me that I was too early. I accepted this, sat down and then realised that she can't be right, I wanted to go and use the lounge afterall. I found a BA staff member near customer services and she escorted me to a free desk and asked the guy to check me in.
It'd be nice if the staff actually knew the rules. I'm hoping that this will have changed since the opening of the Club check in. I'll find out next week....