The Fulcrum interaction with Death's Door

It's a shame these two items don't have their own combination to work together.

If Fulcrum reflects elemental ailment's back to you and Death's Door gives a 50% increase to elemental ailments on you. Should these work together or not?

Its increased duration of ailments on you, not effect (unless that is what you meant).

And it should work but there is currently a bug where lethe shade isnt applying the more duration on reflected ailments. So if it doesnt work I would argue its related to that bug.