Anytime an encounter reads "Return to Arkham" ~ that is shorthand for "you may exit this Other World by a Gate which provides access to this place" I'm being particularly vague, because you need not necessarily "Return to Arkham" from exactly the same Gate you entered.
I'm already familiar with the rule that allows an investigator to exit an OW through multiple gates that connect to the same OW location. But my question is slightly different.
Here's the game situation as it occured:
During the Arkham Encounters phase Micheal McGlen entered a gate to R'lyeh located at Independence Square. This was the only gate to R'lyeh open on the board. Later on during the same phase Sister Mary had an encounter at the Science Building which could have closed the gate to R'lyeh. Being unfamiliar with the rules on this point I decided to skip the encounter.
But what if Sister Mary had managed to close the only gate to R'lyeh? As we've already established Michael McGlen would still have a normal OW encounter phase because he was still in the first section of the OW. If during that phase he were to draw an encounter that said "Return to Arkham", would he return to Independence Square even though the gate has already been closed? Or would he be automaticaly LiTaS?