I had another look at the scene where the camera pans over the map, and it seems to me that 'the Southlands' are slightly to the east and north of the Ered Lithui. Which would make it (just) outside the 'walled on three sides' land that would become Mordor, and (just) inside the southern fringes of what would become known as Rhûn. A fitting place for these descendants of the Easterlings who served Morgoth in the previous age!