The ability triggers just once for each life-gaining event, whether it’s 1 life from Soulmender or 8 life from Meditation Puzzle.

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, Ajani’s Pridemate’s ability will trigger twice. However, if a single creature you control 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.