Coined by Coleen McKechnie, this term is a shortened version of "let's do it."
The basic difference is that "let's do it" sounds like something a boring white man from the north would say. "Lezdewit" is a super-catchy, rolls-off-yer-tongue version that a hot, badass white girl from the south would say.
(The fact that said coiner is a le(z)bian in real life is merely coincidence and has nothing to dew with the spelling nor the word itself.)
Molly: Hey, Tegan and Sara are gonna be at Stubbs next month. You wanna go?
Casey: Hell yeah! Lezdewit!
Molly: So Robin is throwing a party Friday. Five bux to cover yer ass and yer drinks. You down?
Casey: How convenient, I'm thirsty and I just got paid. Lezdewit!
Casey: Yewww cahn dewww it.
Molly: Shut up.
Casey: Weee cahn deww it.
Molly: Shut it.
Casey: Uffryone cahhn deww it.
Casey: Make me.
Molly: Oh yeah? I will...
Casey: Uh... HELL to yer YEAH. bring it beeotch, lezdewit!