Cathy responds, "And Santa is also the word for Saint in many languages. And since the figure of Santa Claus is based off SAINT Nicholas, its not surprising. So nice try, but you failed."
In that case, Sarah caught an L because she tried to prove an invalid point.
'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: 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