How exactly does lethe shade work?

Does it require I stop taking DoT to 're-arm' itself and activate again? Or can I keep it constantly up if i take a new DoT each second?

say i run a Death's Oath setup and it reads 'take X damage for 3 seconds on kill' is lethe shade awesome or useless? (assuming im functionally immune to ailments)

It only works for 1 second after you started taking dot damage of any kind. It only refreshes when you stop taking dot damage for a moment so it's typically useless on builds like RF or deaths oath who inflict dots on themselves. The notable is designed to give you some extra time to react and get out of dots.