Does lifelink apply when a creature deals damage to a planeswalker?

Lifelink is a static ability that causes damage dealt by the creature to also cause its controller to gain that much life (CR 702.15a). This applies to all damage the creature deals — to players, to other creatures, and to planeswalkers — with no exceptions.

When a creature with lifelink attacks and is redirected to deal damage to a planeswalker (or targets a planeswalker directly in some contexts), the damage is still damage dealt by that creature. The lifelink ability triggers off the damage event itself, not off who or what receives it (CR 702.15b).

It is worth noting that damage dealt to a planeswalker removes loyalty counters equal to the damage (CR 306.7), but this does not change the fact that it is still damage for the purposes of lifelink and other damage-related abilities.

Concrete example: You attack your opponent's Chandra, Torch of Defiance with a 3/3 creature that has lifelink. Your opponent does not block. The creature deals 3 damage to Chandra, removing 3 loyalty counters. Because of lifelink, you simultaneously gain 3 life.

Similarly, if your creature with lifelink is blocked and also has trample, any damage that tramples over to the player triggers lifelink for the full damage dealt — both to the blocker and to the player — since lifelink applies to all damage the creature deals in a single combat damage step (CR 702.15a).