I take your point - I think lounge access 2 hours before departure should be available.
I suggest you offer feedback to BA, but I don't think it's their fault - they can't control the police at all, and if the lounge was landside, how many posts would there be about "having to leave the lounge too early for security and then waiting in the terminal for boarding etc."?

In terms of your client, this could turn out to be a positive. I'm sure your client didn't think it was your fault that the passport control people hadn't arrived, or think that it reflected badly on you as an individual, or on your company (not as much as ignoring him to post on FT anyway ) It can be drawn on as a shared experience in years to come and can help cement the relationship.