What the title says. If some creature A with lifelink was blocked by a creature with less toughness than it has power. Do you gain life equal to the blocking creature's toughness or creature A's power?
510.1a Each attacking creature and each blocking creature assigns combat damage equal to its power.
Since toughness isn't mentioned here, it doesn't affect how much damage is actually dealt. You may be getting confused from situations where there are multiple blockers or where the attacking creature has trample; in those situations, the blocker's toughness factors into how the damage can be divided between blockers and/or the defending player, but still has no effect on the total amount of damage to be assigned -- it'll always be equal to the attacker's power.
Everyone knows that good luck and good game are such insincere terms that any man who does not connect his right hook with the offender's jaw on the very utterance of such a phrase is no man I would consider as such.
Since toughness isn't mentioned here, it doesn't affect how much damage is actually dealt. You may be getting confused from situations where there are multiple blockers or where the attacking creature has trample; in those situations, the blocker's toughness factors into how the damage can be divided between blockers and/or the defending player, but still has no effect on the total amount of damage to be assigned -- it'll always be equal to the attacker's power.
----
Lightning Bolts don't kill creatures. State-based actions kill creatures.
- To my youngest sister when she was 6.