I've found several different meanings for Lindsay over the years. As far as I can tell, LindsAy seems to have been the original, with the ever popular LindsEy being a variant, not vice versa. Some of the meanings I've found are:
-Lincoln's wetland/marsh
-Pool island
-Linden island/Island of Linden trees
-As a surname, the eastern part of Lincolnshire was originally called Lindsay/Lindsey, apparently because of the Linden trees as well.
-One random bookmark produced the meaning "peaceful isle"
-Linden trees near the water
I can't really be sure of the believability of all of the sources, but they all pretty much say "island" (if not just some reference to water) and "linden trees".
Any opinions on which one would probably be the right one?