“LULW” is an acronym for “laughing out loud with tears streaming down my face.”
This expresses great amusement and joy at the same time. The phrase also implies that it appeals to emotions in a way that makes the speaker laugh so hard, he suffers from tears of joy rolling down his or her cheeks.
It emphasizes how much this person finds something funny, and wants to express their amusement through laughter. It’s mostly used when someone finds a meme hilarious.