UPDATE: please read the comments on this post for documentation of earlier LOL Cats, including a comment from Jason Scott. This is, sadly, not the earliest LOL Cat known to man.
Digital archivist Jason Scott (creator of BBS: The Documentary) has discovered what might be the first LOL Cat ever. He writes:
From the March 1929 issue of Parents' Magazine, page 73. Someone might call this a LOLcat. Either way, 1920s Nursery Cat Is Watching You Parent.
Ha, Ha, Ha, It must be so!
Photo by Jason Scott, used via Creative Commons license: