We know that Voldemort has threatened Death Eaters in the past, and presumably kept his word. Snape is a former Death Eater, so he would believe Riddle now.

But the claim that Voldemort will return immediately if killed, even if killed tens of times, and can even leave his body at will without dying and possess someone else, is very novel and Snape would have no particular reason to believe it.

Snape would reason correctly that if Voldemort wins, he would punish Snape anyway, for his betrayal during Voldemort's absence. So Snape would try to help Dumbledore and not Voldemort as long as he has a hope of success.

The obvious way to single out Lucius is to provide proof that he wasn't Imperiused to become a Death Eater. Since Riddle is the one who didn't Imperius him in the first place, such proof shouldn't be too hard to find.

This isn't clear to me. Maybe Voldemort can find proof just because he's powerful and good at proof-finding. But it wouldn't be because he didn't Imperius him. Especially since he couldn't present evidence that revealed that it was being presented, or had been collected, by Voldemort.