The ability triggers just once for each life-gaining event, no matter how much life is gained.

A creature with lifelink dealing combat damage causes a single life-gaining event. For example, if a single creature with lifelink deals combat damage to multiple creatures, players, and/or planeswalkers at the same time (perhaps because it has trample or was blocked by more than one creature), Cliffhaven Vampire’s triggered ability will trigger only once. However, if two creatures you control with lifelink deal combat damage at the same time, the ability will trigger twice.

In a Two-Headed Giant game, life gained by your teammate won’t cause the ability to trigger, even though it causes your team’s life total to increase.