Actually I don't think I've ever seen that published, but have been told by a few lounge attendants when entering with someone on a different flight. Could be a 'local' rule that would be pretty hard to dispute should they make an issue of it. Fortunately in the few invites I've had where my companion was on a later flight it's never been raised.

The only time I've ever had the lounge staff really police it was one time at the UA Club somewhere domestic, might have been ORD or DEN, can't remember but I was on an international ticket as a 1K (self + 1 guest allowed). Someone in front of me was trying to get in on a Chase Pass that was expired, so I just said I'd guest her in. First they got in a huff and asked if we knew each other, so I just said yes and the other passenger played along. Then they made a strong point that she must leave the same time I did, so we just said ok and went on our day. I don't think they can really deny access just because we met 5 seconds before, that's not in the rules, but is of course against the spirit of guesting someone. The agent clearly didn't like it.