I flew in J form LGW to DFW the day after the move to the north terminal. My experience:

at check-in I was given an invitation to the Terrace.
as an EXP I proceeded to the F lounge, handed in my Terrace invitation, had my BP swiped and was warmly welcomed.
I moved between the F and J with ease, just told the door staff I was already signed-into in the F lounge (and had my BP in case they wanted to see). No probs, no looking me up in the computer or anything. I beleived it helped that I was well dressed - like everyone else in the F lounge.

I have no idea what would happen without the Inv for someone without OW lounge access status. may be a real problem for connecting pax who don't have to check-in in LGW