1) A sauce-like product created from too much laughter.
2) An overexaggerated version of 'lol', usually used by nubs or by people mocking nubs.
Subject A: "...And then he shat himself!"
Subject B: "Dude, I'm laughing so hard I made lawlsauce!"
Subject A: "...Ew?"
Gamer A (Nub): "Lawlsauce! That was great, we like owned his shiznit! Or whatever."
Gamer B: "Yeah...ok. Not really."
Having created so much laughter, a bottle of "lawlsauce" is spawned.
Such a term is used when there is extreme laughter with or at someone.
WOULD YOU LIKE SOME LAWLSAUCE WITH THAT OWNAGE?
Hang on, I need to get a bottle of lawlsauce.