If you gain an amount of life "for each" of something or "equal to the number" of something, that life is gained as one event and Vampire Scrivener's first ability triggers only once.

Each creature with lifelink dealing combat damage causes a separate life-gaining event. For example, if two creatures you control with lifelink deal combat damage at the same time, Vampire Scrivener's firstability will trigger twice. However, if a single creature you control with lifelink deals combat damage to multiple creatures, players, planeswalkers, and/or battles 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 or lost by your teammate during your turn won't cause either of Vampire Scrivener's abilities to trigger, even though it caused your team's life total to increase or decrease.

If Vampire Scrivener is dealt lethal damage at the same time that you gain or lose life during your turn, it won't receive a counter from its ability in time to save it.

The first ability of Vampire Scrivener triggers just once for each life-gaining or life-losing event, whether it's 1 life from Dazzling Angel or 4 life from Apothecary Stomper.