Looks like it's one of those idioms with the letter, like "dot the i's and cross the t's". "Like L's" here most likely refers to the shape of this letter. "Like lazy L's" then means "reclined back, or even limp of a sofa/armchair" By the way, when one is learn how to play chess, they are said that a knight goes in an L shape, which also implies shape.

I'm guessing it refers to the shape of the letter L. Lazy, because it's tipped back, reclining - a bit like this. \_