The ability triggers just once from each life-gaining event, whether it’s 1 life from Soulmender or 5 life from Elixir of Immortality.

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, Archangel of Thune’s ability will trigger twice. However, 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), the ability will trigger only once.

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.