This implies that, powerful as the Lich King is, he's ultimately just an empowered undead mortal, and that power is ultimately derived from a demon (who is himself a former mortal.)
But there are a couple things that have never really sat well with me. In Warcraft Chronicle, there's a chart that delineates six primal forces that each have an associated type of magic. The one generally see as "good" are Light, Life, and Order, embodied by Holy, Nature, and Arcane magic respectively. The "evil" ones are Void, Death, and Chaos, embodied by Shadow, Necromancy, and Fel magic, also respectively.
In the game, however, we've tended to see Void and Chaos as the two really grand pillars of Warcraft villaindom. The Void Lords and their creations, the Old Gods, seek to corrupt the universe with Shadow, while the demons of the Burning Legion use Fel magic to try to utterly destroy the universe.
(Side note: one would think that the servants of the Void (described by Star Augur Etraeus as "avatars of non-existence") would be more into utter universal annihilation while the demonic Fel force would seek to corrupt it. But it could be we're just not seeing the long game here.)
Death as a force, however, doesn't seem to get the same kind of top billing as Void and Chaos, but perhaps that's something Blizzard will remedy in the future.
The origins of the Lich King's necromantic powers are somewhat enigmatic. We know that Fel-affiliated demons and warlocks have performed necromancy in the past - consider the original Death Knights, for example, who were created by Gul'dan. And so perhaps it wouldn't be too crazy to think that Kil'jaeden could tap into necromancy to create the Lich King.
On the other hand, seeing Ner'zhul B in Draenor showed us that using Shadow magic, one can also raise the dead, as we saw in Shadowmoon Burial Grounds.
So maybe I'm getting too hung up on that chart, but if we want to run with it, it would seem to suggest that necromancy really is its own thing, not beholden to Shadow magic or Fel magic.
Considering that the Burning Legion employs Voidwalkers (there's a whole section to the Broken Shore that's purple-void-corrupted rather than the usual green-fel-corrupted) despite the fact that such beings are theoretically the exact thing the Legion was founded to defeat (though in a Halo-like "cutting off the food supply" manner,) it wouldn't be that odd to think that Kil'jaeden dabbled in other kinds of magic.
But the explanation that I prefer, and I think that Blizzard would benefit a lot from in terms of future story potential, is that Necromancy is, in fact, totally independent, and the the Lich King, or whatever dark entity that served as the basis for the Lich King, existed long before Kil'jaeden got involved.
Now, it's also possible that some "prime representatives" of these primal magics still owe their origins to others. The Druid artifact backstory implies that the Wild Gods (aka Night Elf Ancients, Pandaren August Celestials, and Troll Loa) were originally just ordinary animals that Freya (yes, the one we fought in Ulduar) empowered and linked to the Emerald Dream. And while he was once a mortal, Kil'jaeden is now a being of nearly god-like power (the Warcraft universe is pretty strict on who gets to be called a god, though that's getting looser, with the Titans getting confirmed god status - albeit non-immortal gods) so if someone like Freya could create beings of such power, Kil'jaeden ought to be able to do so as well.
Still, I think there are elements of the Lich King that we really have not explored yet. Chronicle Vol. 2 ends right before the Third War, so we don't get anything about the Lich King.
In addition to the primal power of Death, there are a couple of other sort of related concepts in that chart of magic and planes. Moving to the elemental plane, there's two forces in addition to the four basic elements. One is Spirit, which is aligned with life, and is used by Shamans as a kind of binding agent for the four elements and is used by Monks as their primary power on which they draw (they call it Chi.) Spirit is demonstrably powerful - the Elementals on Azeroth are so chaotic because the Titan world soul requires so much of it to grow. Meanwhile, on Draenor, with no world-soul and an abundance of Spirit, the plantlife grew so powerful that it threatened to overwhelm its own resources and ironically wind up starving itself out of overgrowth, which is why Aggramar created a giant who was the ultimate ancestor to the Magnaron, Gronn, Ogron, Ogres, and Orcs.
The opposite of Spirit is something called Decay, which, unlike the harmonious Spirit, is all about force. Dark Shamanism is distinguished from classical shamanism because of its emphasis on this. While a typical Shaman beseeches the elements for aid and is something of a conduit for consensual elemental power, Dark Shamans enslave the elements to do their will. The result, as we saw with the Korkron in Mists of Pandaria, is that Dark Shamanism leads to environmental damage - polluted air and water and treacherous earth.
Finally, getting to the real semi-physical planes, we get one that is truly associated with death: the Shadowlands. While the Emerald Dream is a place of vibrant life (except where the Nightmare corrupts it, though I think we've officially destroyed almost all of the Nightmare,) the Shadowlands are an empty and cold land of death.
It has never been officially confirmed, but there is very strong evidence that in-game, if we die and go into ghost form, we're actually running around in the Shadowlands (and that the Spirit Healers are actually rogue Val'kyr who defied both Odyn and Helya for the sake of the greater good, namely returning the heroes of Azeroth to life so that we can continue protecting the world.)
If the Emerald Dream is the domain of the Wild Gods, it would stand to reason that the Shadowlands would have some sovereign. A King, if you will.
Now, perhaps that Sovereign was actually Helya - Helheim's location isn't ever really defined, and could be its own plane (we also don't know where the Halls of Valor are, exactly) and given that Helya assisted Ra-Den in creating the Elemental Planes, it's not that hard to imagine her creating Helheim from scratch.
But Helheim certainly looks like it could be a part of the Shadowlands.
Still, if we're talking about Death as being a primal force that is independent from other primal embodiments like Old Gods, Titans, and Demons, it seems to me that you could imagine there being some entity within the Shadowlands that was the embodiment of death and necromancy.
And perhaps that entity was amorphous - not in any way human-like. Perhaps Kil'jaeden poured that entity into Ner'zhul not just as a weapon, but also as a way of controlling an entity that was likely more powerful than Kil'jaeden himself.
And this actually begins to explain why "there must always be a Lich King." It wasn't really clear what the Scourge "running rampant" would look like, given that they weren't exactly friendly at the time, but maybe we really haven't seen anything yet.
Prior to the Lich King, this Death God was in the Shadowlands - incredibly dangerous but safely in its own realm. Kil'jaeden sought to use its power for the purposes of the Legion, but simply releasing it into the prime material plane would have meant undeath spreading everywhere - perhaps even to demons (and while the Legion's official mission is universal annihilation, but their actions suggest their actual goal is more a kind of universal tyranny - which requires subjects.) The Lich King thus may be a kind of de-powered Death God - something that the people serving as the Lich King may only know to varying degrees.
Kil'jaeden pulled the Death God out of the Shadowlands, putting it in a humanoid-shaped (or armor-shaped at first) vessel to ensure that it didn't escape and simply wash over everything and to ensure that its power could be used productively by the Burning Legion.
So then this opens questions as to what the longterm goals of Bolvar are. He nominated himself to be Jailor of the Damned, which seems like it would mean especially controlling the Death God within himself. But we don't know if he's been as effective at holding out against this influence as he was in the past. He's definitely not a good person anymore, but one really has to wonder what our actions as Death Knights have been doing for his goals. We recruited the Four Horsemen - who seem to serve the Lich King, rather than us Deathlords. And even Darion Mograine has been raised from the dead a second time - which means that his break from the Lich King's control after the Battle of Light's Hope may no longer be in effect! As the folks at Blizzard Watch pointed out in their latest Lore Watch podcast, when we start the expansion, Darion tells us explicitly that we're getting assistance from the Lich King, but we're not rejoining the Scourge. And yet, and yet, every action we take to empower the Ebon Blade is actually making the Scourge more powerful.
Now it's possible that being part of this Bolvar-era Scourge will ultimately be good for Azeroth, even if we do things to seriously piss of the Silver Hand and the Red Dragonflight and anyone else who gets in our way.
But the Deathlord may have really screwed things up and will have a serious price to pay when he or she looks around and finds that all of his comrades are now getting conscripted into the Death God's campaign to wipe out all life on the planet.