If you aren't exhausting the heat from the AC out of the lung room, it will most definitely not have a cooling effect. The AC unit creates more heat than cold.
Regardless, you need to control the climate of the entire lung room. Since the tent is exchanging air with it, the temp/rh% inside the tent is relative to the lung room, even if it's a slight offset due to rate of gas exchange between tent and encompassing room.
So, the window ac unit needs to go in a window and exhust outside. Hence, "window" unit ... it's in the name for a good reason. Unlike a "solar" cover for a pool, which has nothing to do with sunlight as far as how it functions.