Does lifelink apply to damage dealt by a creature to another creature in combat?

Lifelink is a static ability that causes a player to gain life whenever the creature deals damage, regardless of the damage's source or target. This is stated in CR 702.15a: 'Lifelink is a static ability that modifies the rules for damage.' The gain occurs simultaneously with the damage being dealt, not as a triggered effect.

CR 702.15b specifies: 'If a source with lifelink deals damage, its controller gains that much life.' There is no restriction on what the damage is dealt to — it applies to damage dealt to players, planeswalkers, battles, and yes, other creatures in combat.

CR 509.2 governs combat damage assignment and dealing. When a creature with lifelink deals combat damage to a blocking or blocked creature, the lifelink effect applies to that damage in full. The controller gains life equal to all combat damage dealt, even if the damaged creature is not destroyed (for example, if it has more toughness than the damage dealt).

Concrete example: You attack with a 3/3 creature that has lifelink. Your opponent blocks with a 5/5 creature. Your creature deals 3 damage to the 5/5 (which survives). Even though your creature is destroyed by the 5/5's 5 damage in return, you still gain 3 life from your lifelink creature's damage.

Note that lifelink applying to combat damage between creatures is different from older 'life gain' triggered abilities — because lifelink is a static ability, the life gain cannot be responded to with instants in between the damage and the gain (CR 702.15b).