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.

The ability triggers just once for each life-gaining event, whether it's 1 life from an attacking creature with lifelink or 4 life from Faith's Fetters.

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