I recently discovered that one of my friends with whom I often instant message is not always "laughing out loud" when he types the initialism "lol." In retrospect I know I shouldn't be surprised, but it always delighted me to imagine that the thing I'd typed moments before was so funny that he was unable to control himself, in fact so funny that he couldn't master the coordination to type anything but those two letters, conveniently located adjacent to each other. But this is not the case. This weekend, while he was on gchat I watched him type "lol" after a friend sent him a message that wasn't even remotely funny. Which filled me with doubt. Am I really not funny?
I have never typed "lol" myself when I have not just laughed out loud. Do I perhaps have a problem with being too literal? Almost certainly the latter. Clearly the "lol" is a symbolic meme. There are currently no published studies that determine just how many people are actually laughing out loud and I think it's safe to assume that the percentage is low. However if that's the case I don't know how "lol" overturn "haha."
"Haha" has the benefit of adaptability. An extra "ha" may be added at either end to convey more amusement, or reduced to a single "ha" to express a dryer and lighter sort of humor. Lol lacks that flexibility. Perhaps convenience is king: "L" and "o" touch each other on the keyboard while your fingers must travel to write "haha." Or maybe it's appealing because it's one pronounceable syllable. But neither consideration has impeded the popularity of other initialisms such as "lmao" and "lmfao." Furthermore those are clearly meant to be hyperbole for the sake of further amusement. But "lol" can be taken literally and thus using it so freely seems disengenous.
More about "LOL" here.