I'm not sure if anyone found this before but I received a mail from Gunnie who spotted this map fragment in S04E11 and was able to identify the islands illustrated on it. Thanks a lot, Gunnie!
Just watched S04E11
At 34:55 Jack pulls out a map from the bag that Lapidus dropped from his chopper.
The map is of Tarawa atoll in the Republic of Kiribati…
Tarawa is located at Latitude 1°22'47" N, Longitude 173°09'06" E
USA used this area for nuclear testing and the republic is now days the first nation we expect to disappear due to global warming.
I guess that the island (before it moved) was close to Tarawa, since Lapidus had folded the map like that.