For a non-lethal run, do I need to keep bodies off the ground?

In Dishonored 1, if you left an unconscious body on the ground it was likely that rats would eat it, leading to an unintended kill. So every time I did a non-lethal takedown, I had to look around for a shelf, roof, or dumpster where I could safely tuck my sleeping victim.

Is that necessary in Dishonored 2? I haven't seen rats swarm on a corpse yet, and since there's not a rat plague hopefully they won't. But I'd hate to mess up a non-lethal run by accident.

Yes; in Dishonored 2, rats can still eat unconscious bodies, which will count as a kill in your mission stats (in the pause menu), just like in the first game. In fact, this time rats will eat bodies even if there are only 4 or 5 of them running around (which, in Karnaca, there usually are as you've implied from your rat plague comment).

I've noticed, however, that this does not apply to

rats eating unconscious Nest Keepers,

and it's unclear to me if that is intentional or an oversight.

If there are only one or two rats, though, it shouldn't be a problem. Not all groups of 4 or 5 rats eat bodies in my experience, but it was quite a rude surprise to find out that some were doing just that.

Unconscious bodies are naturally still susceptible to damage — for example, in mission 3, two guards on a staircase are dangerously close to lanterns, and may burn to death if you knock their bodies.

As for rats, I'm not entirely sure, but bloodflies will definitely eat bodies. As a game tip itself says, "bloodflies will eat bodies before attacking you. Use this to your advantage."