Cindering Cutthroat

Creature — Lizard Assassin

This creature enters with a +1/+1 counter on it if an opponent lost life this turn.

: This creature gains menace until end of turn. (It can't be blocked except by two or more creatures.)

Cindering Cutthroat's first ability cares whether an opponent lost life this turn, not how their life total changed. For example, an opponent who gained 2 life and lost 1 life in the same turn still lost life.
Once Cindering Cutthroat has been blocked by a single creature, activating its last ability won't cause it to become unblocked.