From YouRememberThat.com, a 1905 postcard that may be the oldest extant LOLcat:
The source suggests:
Perhaps soon, archeologists will discover an even older LOLcat on the walls of an Egyptian tomb… perhaps a cat with the caption, "I see what you did there!"
But it seems to me that if there are Egyptian (or Sumerian, or Mayan, or Mycenean, or Etruscan, or …) LOLcats, they've probably already been dug up and are now lying on some dusty museum shelf, waiting to be revealed to the world by a scholar who reads Language Log.
[Hat tip: Randy Alexander]
[Update — commenters (below) have informed us that this appeared last December on icanhascheezburger.com, and that this was one of a large number of similar proto-LOLcats produced by Harry Whittier Frees (1879-1953), a sample of which can be found here.]