Does a spell that says 'destroy all creatures' count as a single source of damage for lifelink?

Lifelink is a triggered ability that causes a player to gain life whenever a source with lifelink deals damage (CR 702.15a). The key word here is damage. A spell that says 'destroy all creatures' does not deal any damage — it simply moves creatures from the battlefield to the graveyard as a state-based action following the spell's resolution (CR 701.7a).

Because no damage is dealt by the spell, lifelink has nothing to trigger on. It does not matter whether the effect hits one creature or a hundred; if the word 'damage' never appears in the process, lifelink does nothing.

This is a common confusion because board-wipes and damage-based sweepers look similar in outcome (lots of creatures die), but the rules treat them very differently. A spell like Damnation destroys creatures; a spell like Blasphemous Act deals damage to creatures. Only the latter interacts with lifelink.

Concrete example: You control a 3/3 creature with lifelink. Your opponent casts Damnation ('Destroy all creatures'). Your creature is destroyed, but because no damage was dealt, lifelink does not trigger and you gain no life.

If instead your opponent cast Blasphemous Act ('It deals 13 damage to each creature'), and your creature with lifelink survived somehow and dealt damage in the same step, lifelink would apply to any damage your creature itself dealt — but still not to the damage Blasphemous Act dealt, since lifelink only cares about damage dealt by the lifelink source (CR 702.15a).