There's another category, arrival lounges. I've been to the one at CDG and am told there is a similar one at (at least) LHR. These are after clearing passport control and customs, and are for Business/First pax only. Status won't get you in if you arrive in Economy.

There seems to be an open question as to whether arriving passengers can use Flagship Lounges. I've been let into the one at ORD, but others have reported being turned away from them (perhaps not at that one).