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If you gain life at the same time Blood Researcher is dealt lethal damage, it dies before its ability can put a +1/+1 counter on it.

An ability that triggers “whenever you gain life” triggers just once for each life gain event, no matter how much life you gain.

Each creature with lifelink dealing combat damage causes a separate life gain event. For example, if two creatures you control with lifelink deal combat damage at the same time, a “whenever you gain life” 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.

If you gain an amount of life “for each” of something, that life is gained as one event and the ability will trigger only once.