Basically, he's using humor (maybe it doesn't translate well) to describe a horrible situation, a disaster.
Lice are little insects, like fleas (those little bugs that make your dog itch and scratch). So that's not a nice thing. And neither are rats. So lice + rats is already bad. A corpse is a dead animal. Also not good. So one disgusting thing (lice) on another horrible thing (rats) on another horrible thing (dead horse)... and the horse is on fire, it is burning, like dead horse BBQ. Pretty horrible as well. It's a pile of ugly metaphors: add them up, and you have a disaster.