If when I sacrifice door to nothingness I would lose enough life to lose does its ability resolve first or do they happen at the same time giving us a tie?
The door is activated and resolves at instant speed. What damage are you taking from what. Is it a {lightning bolt}, {lava axe}, or attacking creatures?
Stack: first in is last out
If your door was the first thing in and they figure out a way to kill you or some trigger kills you at instant speed then thats it you lose. However if you activate door in response to something that would kill you then they lose.
RESOLVED
{door to nothingness}