Nekron is "Lord of the Unliving" and the ruler of a dimension where souls go after they die, although this is clarified as "before their final judgment". If Death of the Endless is also present in the DC Comics (or Detective Comics Comics) Universe, how is her/his/its dominion over death (and her/his/its task of shepherding the dead) reconciled with Nekron's powers, existence, dimension and his Black Lantern Corps?
Really, Sandman can be considered 99% distinct from the DC Universe. The characters from Sandman don't interact on any significant level with the 'traditional' DC heroes, and Gaiman's characters just don't show up in DC's books.
That said, Nekron is nothing to Death. Death isn't a character, Death is an idea. The last idea, possibly. She doesn't have motives, she doesn't have desires, she doesn't have dreams. She just ferries.
Nekron's Black Lanterns seem to be undead. Death doesn't care about undeath. Death doesn't care if you are resurrected. Death doesn't fight Nekron for souls, howling when they are rent from it's grasp and forced into corpses. Death simply waits.
Death has taken Gods, lost gods, forgotten gods, new gods. Death will take Superman, Batman, Zeus, Flying Spaghetti Monster, Nekron, Desire, Dream, and, finally, when the Universe has wound down, Death.
Death is an idea, a concept, an irresistible force which came into being the instant the first form of life did. Nekron is nothing. And at the End, Death will "put the chairs on the tables and turn out the lights as [she] leaves." Nekron will have been completely forgotten, irregardless of his powers, his Corps, or his dimension.
In the DC Universe, the two entities Death and Nekron have very little to do with each other beyond both being related to the conceptual idea of death and dying and possibly having an existence that predates the current Universe. Curiously enough, both ARE concerned with Death, but their outlook on the implementation of that outlook is their primary difference.
As far as their relationship? Things die. Death sees to it. They eventually get shepherded to their respective afterlife. Those who find themselves in-between their paradise or punishment in the afterlife, find themselves hosted by Nekron in a purgatory (it is unclear if there is more than one purgatory) until such time as they move on. Purgatory was never meant to be a permanent condition. Though Nekron is the master of this Land, his control of it does not seem to disturb Death of the Endless, so he must be serving a purpose beyond mortal understanding, perhaps without even realizing it.
It is unclear whether Death can die. Though she has incredible magical might and some level of omniscience, she is without fear, strangely moral, and despite this remains the most cheerful member of the Endless.
Nekron is more concerned with subverting death, returning the dead to a semblance of life, so he may further his goal of bringing death to the Universe at large, the sooner, the better. No one knows his origin or how he came to become lord of the Land of the Unliving.