If a creature you control dies at the same time that your life total becomes 0 or less, you lose the game before Overgrowth Elemental’s last ability can save you.

If Overgrowth Elemental dies at the same time as one or more other creatures you control, Overgrowth Elemental’s last ability triggers for each of those other creatures. You will gain 1 life for each of them, but if any of those creatures were Elementals, Overgrowth Elemental won’t get a +1/+1 counter since it’s already left the battlefield.