It only happens at those lounges where there is something like an Aspire like operation happening to non BA customers and some lounge agent is enforcing time limits on the commercial customers and gets swept up away with it. The protocol seems to apply to people arriving very early before a flight departure time, rather than staying too long after an irrop. I noticed that there is some verbiage about this at the T5 Aspire lounge, and when you book online you are booking a specific arrival / departure time.

For BA I've never experienced or seen this happen. On my Vueling Pass card at the Europa Lounge in Munich they did once say something like "well you're a bit early" at about 3 hours before departure, coming off a connection, but they weren't that bothered. For BA run lounges there is supreme indifference, the internal charging is based on entry headcount rather than entry headcount hours.