Does a creature that deals damage via a triggered ability benefit from lifelink?

Lifelink is a static ability defined in CR 702.15a: whenever the creature deals damage, its controller gains that much life. The key word is the creature dealing the damage — lifelink attaches to damage events caused directly by the creature (combat damage, or damage it deals via its own activated abilities that say 'this creature deals damage').

When a triggered ability deals damage, the source of that damage is the ability itself (or the object that created the trigger), not the creature as an actor dealing damage in the normal sense. CR 609.7 clarifies that a spell or ability that deals damage is distinct from the object that has lifelink. Lifelink does not spread to damage dealt by separate triggered abilities, even if they are printed on the same card.

For example, consider a hypothetical creature with lifelink and a triggered ability that reads 'When this creature attacks, it deals 2 damage to any target.' That triggered ability fires and resolves as a separate game event. The 2 damage is dealt by the ability, not by the creature dealing damage in the way lifelink tracks. Your opponent loses 2 life, but you gain no life from lifelink.

Compare this to a creature with lifelink dealing combat damage or being the source referenced in an activated ability like '{T}: This creature deals 1 damage to target creature' — in those cases the creature is the damage source and lifelink applies (CR 702.15a, 119.3).

In short: lifelink only triggers off damage events where the creature itself is the designated damage source. A triggered ability that deals damage is an independent source, so lifelink does not apply.