The new LOL ; point of all abbreviations is to be short and meaningful. L = Laugh, effective in responding to random nonsense, and could be used effectively in a sarcastic tone as well.
'L' works better than 'LOL' because it can be used in a variety of responses more effectively. Just saying 'I Laugh' is saying this could be funny, lame or useless - you are not 'laughing out loud'. It is rather that what is said in the statement is laughable.
Austin: That was funny! LOL!
Austin: I cant dance
Sarah: I love you
Drake: I love you too :)
Austin: I lost all my money
Austin: I just won a million dollars
Drake: No way, congrats man
Austin: What a dumbass that guy was