If a creature has lifelink and is blocked by multiple creatures, does lifelink trigger for each creature it deals damage to?

Lifelink is a static ability, not a triggered ability, so it does not 'trigger' at all (CR 702.15a). Instead, it modifies the rules for how damage works: whenever the creature deals damage, its controller gains that much life as a replacement/addition to the damage being dealt (CR 702.15b).

When a creature with lifelink is blocked by multiple creatures, it assigns its combat damage among those blockers according to CR 510.1. All of that combat damage is dealt simultaneously (CR 510.2). Because of lifelink, the total damage dealt across all blockers causes the attacking player to gain life equal to the sum of all damage dealt.

For example: your 5/5 lifelink creature is blocked by a 2/2 and a 3/3. You assign 2 damage to the 2/2 and 3 damage to the 3/3. When damage is dealt, you gain 5 life total (2+3) all at once — not in separate increments.

This also means lifelink works the same way if your creature deals damage to both blockers and, say, a planeswalker via redirection, or in any other multi-target scenario: you gain life equal to all damage dealt by that creature in that combat damage step.

Key rules: CR 702.15a (lifelink defined as static ability), CR 702.15b (life gain tied to damage dealt), CR 510.1–510.2 (combat damage assignment and simultaneity).