No it was a small carrier with few partners. And the family member didn't even have that boarding pass in hand yet. But even if there had been no connecting flight at all, the pass should have been honored.
Denying lounge access to someone who just walked off an 11-hour United flight (not to mention the preceding feeder United flight) is a customer-hostile policy.
The length of flight is irrelevant. Access rules are access rules. However I'm curious who this small carrier with few partners is that flies from LHR T-2. Carriers I'm aware of as of today that use T2 are all major airlines, partnered in alliances....which is back to being *A centric. The condensed T-5/T-2 operations in place at the height of covid have largely eased, except for T-4 remaining closed. The person would have had disembark their flight, go to T-2A to go back thru transit security, clear transit immigrations, and head all they way back over to T-2B to get to the UC. This is a process and it takes time. You cannot walk directly off a flight from the USA into the UC at LHR. All paths lead thru T-2A and some form of immigrations. Oh, and you'd have to have a boarding pass to get back thru security which apparently they didn't have...only a used pass or two. I'm not even going to mention the fact that if the next flight was a non *A/partner carrier and they had checked bags they wouldn't interline and they'd have to claim them...which renders what I said about the transit security etc moot. Quite a lot of work just to go to a UC. Personally I'd have squared away my connection and gotten a boarding pass for it before I ever thought of fooling around with UC access.