Hi! I'm Marlene! When I LOL at you, it means I didn't actually read your joke. When I HAHA, it means I thought your joke was trash.
Only on the rarest of occasions do people use "LOL" literally, to mean they're actually laughing out loud. Most of the time, it's used as a general acknowledgment of humor. You noticed that the person you're texting said something that registered in your brain as a joke, but it didn't draw any kind of physical response from you. From the outside, there's nothing but indifference. In response, you type "LOL." It's a digital doggie treat: "You made a valiant effort at being funny; here's a reward."
"Now lick the peanut butter ..."
On the other hand, when someone texts you something that is genuinely funny and actually does get a physical response, the response that feels most appropriate is "LOL." Its usage is muddled by its rampant misuse.
If I'm meeting you for the first time and there's even a sliver of a chance that we will become close enough to communicate via text message, I want to know your primary definition of "LOL." I want to know if you're the kind of person who tosses it out with no regard for what that acronym can do to a person's ego. If we're texting and I say something somewhere in the area code of funny, are you going to throw me a "LOL" bone, or are you withholding your "LOL"s until I one day say something so goddamned hysterical that the only way to convey the level of nonstop hilarity you're in the midst of is by reducing the English language to base elements, hoping just three letters can encapsulate the euphoric laughter you're experiencing?