Help please.. because I always rush to find I have missed lounge access because I got out too soon from a terminal when reaching another one.

I am reaching TBIT on a LH Biz class and have almost 6 hours layover connecting to UA biz/first flight to PHX. I would rather want to spend my time in the *A biz lounge than anything in T7. I have global entry. Would I be allowed to access the TBIT *A lounge with my onward boarding pass? Or must I have to get out to do immigration and customs? I only have carry-on (no check-in luggage to pick up).