Does lifelink apply to damage dealt to planeswalkers?

Lifelink is a static ability that causes damage dealt by the affected permanent or spell to also cause its controller to gain that much life (CR 702.15). The key rule is that lifelink triggers on damage dealt, regardless of what is being damaged — players, creatures, planeswalkers, or battles.

When a creature with lifelink attacks and the defending player redirects that damage to a planeswalker they control (or when the creature attacks the planeswalker directly, as is the rule since the Planeswalker redirection rule was removed in 2019), the damage is still being dealt by the lifelink creature. Therefore the lifelink controller gains that much life (CR 702.15a, CR 120.3).

It does not matter that the planeswalker is not a player or creature. Lifelink cares only that damage was dealt by the source with lifelink, not what received the damage.

Example: Your 3/3 creature with lifelink attacks, and your opponent blocks with nothing, choosing to let it deal 3 damage to their planeswalker Jace. You still gain 3 life from lifelink, even though the damage went to the planeswalker and not directly to your opponent.

Note: Since 2019, planeswalkers are attacked directly rather than via redirection (CR 306.7), but the lifelink interaction works the same either way — damage dealt is damage dealt.