It would seem that LOL cats were probably the brain child of Harry Pointer, a photographer based in Brighton during the 1870s. He lovingly took photos of his pet cats, eventually setting them in silly poses like riding bicycles and balancing on a skateboards. To add to the cheesiness, he added little captions to each shot. Not surprisingly folks flocked to buy these daft photos, eventually Pointer had them made into greeting cards and by 1884 the Brighton Cats collection expanded to include around 200 LOL kitties.
You can read more about Pointer and his Brighton Cats Collection here.