Does lifelink from a static ability apply to all damage a creature deals or only combat damage?

Lifelink is a static ability that modifies the result of any damage event the creature is involved in as the source. Per CR 702.15b, whenever a creature with lifelink deals damage — from any source or game action — its controller gains that much life simultaneously with the damage being dealt.

This means lifelink triggers on combat damage, damage from activated abilities (like a Prodigal Sorcerer's tap ability if it had lifelink), damage from triggered abilities, and even damage dealt by the creature as part of a spell effect. The damage type does not matter; what matters is that the creature with lifelink is the source of the damage.

It is important to note that lifelink is a static ability, not a triggered ability. The life gain happens as a replacement-style modification to the damage event itself, not on the stack afterward (CR 702.15b, CR 119.3f). This means it cannot be responded to separately.

Concrete example: You control a Fireshriker (a creature with lifelink and first strike). During your opponent's turn, an opponent controls a creature with an ability that reads 'Deal 1 damage to target creature.' If that creature were enchanted to gain lifelink, it would still only trigger on damage it deals. But if YOUR lifelink creature uses a tap ability to deal 2 damage to a planeswalker, you gain 2 life — that's non-combat damage still covered by lifelink.

Bottom line: there is no distinction between combat and non-combat damage for lifelink. Any damage dealt by a permanent with lifelink causes its controller to gain that much life (CR 702.15b).