2/3 with lifelink deals damage to 1/1 does it gain 2 life

[smilon]

2/3 with lifelink deals damage to 1/1 does it gain 2 life

[Kenji]

"It" meaning the creature itself? No, creatures don't gain life themselves; players do. So, I'm assuming you actually meant, "does its controller gain 2 life?"

If so, the answer is yes. Creatures don't pull their punches -- your Vampire Nighthawk (the only 2/3 creature with lifelink that comes to mind) will always deal 2 damage in combat, regardless of the toughness of the opposing creature(s), which results in 2 life gained. The only way this changes is if the damage is prevented, increased, or decreased by an outside effect.

So, assuming no combat tricks from either player, your Vampire Nighthawk deals 2 damage to the 1/1 that it's blocking or blocked by., resulting in you gaining 2 life.