How does Wizard's Lightning stop Archfiend's Vessel?
Wizard&#39;s Lightning was surely used in response to Archfiend&#39;s Vessel's triggered ability, which means the spell was cast and resolved after the ability triggered, but before the triggered ability resolved. The Archfiend's Vessel is on the battlefield as a 1/1 until its triggered ability resolves, and thus easily succumbs to Wizard's Lightning.
The triggered ability does go on to resolve, and it does attempt to exile Archfiend's Vessel, but it fails to do so since Archfiend's Vessel doesn't exist anymore.[CR 400.7] And since Archfiend's Vessel can't be exiled, the &quot;if you do&quot; clause is false, and the Demon isn't created.

400.7. An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence. There are nine exceptions to this rule: [None of them are relevant here.]

A ruling on Gatherer confirms this conclusion.