Was the donkey actually shot irl?

That would never be allowed

I think the kill was real. I watched the credits, there was no "no animals were harmed or killed" there. Nope.

It's certainly cheaper to buy a donkey than to animate that.. Another donkey or pony approaches the dead/dying one, so it couldn't have been just pixels, unless both were, but no I don't think so. It is getting harder to tell if humans or animals are animated, but you can still tell.

I always worry about these things, too. Maybe this will make you feel better. The donkey was not killed.
It was anesthesised for the scene.

http://www.irishexaminer.com/lifestyle/features/the-locals-in-sneem-talk-about-the-filming-of-the-lobster-movie-in-their-region-357086.html

I see no reason not to shoot it with a tranquilizer.

there's a highway that is curling up like smoke above her shoulder

I don't think they would have been allowed to do that, on film like that. I know that animals are killed in slaughterhouses and stuff, but most people don't see that, and it isn't filmed as evidence.

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http://www.youtube.com/watch?v=GAIJ3Rh5Qxs

No, of course not. And they didn't actually kill the dog in real life, either.

if you look closely you can see it can barely stand before she starts shooting and that it starts to fall before she fires the first shot.

Yep.

And the other donkey didn't react to the sound of a gun being fired at all... 😁