Ok here we go.
I found myself struggling a bit more with this than I had thought.
One reason is the one stated above: those categories are made for individuals. By D&D standards there can't be armies of CE individuals for example.
The other reason is that I am in fact not very knowledgeable about AoS lore either, so for some factions I don't really know and might misjudge them.
Anyway, let's start. I made a list because creating graphics on my phone is a pain in the behind.
LG: Seraphon might actually apply.
They don't usually interfere, but when they do they do so out of altruistic reasons. They are very ordered, and pretty reliable.
That being said: they could fit LN, too.
LN: maybe Stormcast Eternals.
They are very ordered, and they adhere their rules, but _only_ their rules. They are seen as the good guys, but many of them aren't. They do pretty good things, and very evil things, because they see them as justified.
LE: Kharadron Overlords.
This is one of the easier ones because they are greedy traders. They would do almost anything to satisfy their needs, and they don't care with whom they trade. They seem to strictly adhere to their rules and laws though, and they do have an ordered structure in their society.
NG: Cities of Sigmar
NG is one of the more common alignments. Many people might be selfish enough to be NE, but many are altruistic enough to qualify as NG. As a whole I think the Cities of Sigmar, a conglomerate of species that tries to help each other survive in a brutal world but don't necessarily adhere to all the rules, should fit NG.
NN: Sylvaneth
They fight Chaos. But they also fight everyone else who gets into their way. They rarely attack though, except in great need. They don't care much for the others. They sometimes act altruistic but they also have very evil beings within their ranks (Spite Revenants for example). As a force of nature I would call them true neutral.
NE: Legions of Nagash
Tough. Traditionally Liches and the like are CE, they care only for themselves. And that might be true for Nagash, because all the other undead are just tools for him. However as a whole I would call them Neutral Evil. Think of all the living practitioners of Death magic, all the Vampires and Necromancers and Ossiarch dudes, they form armies and have ordered structures. Judging by the Malign Portent stories I'd even I'd even say that some of them have altruistic feelings. That's just not chaotic enough for CE. They want to rule the world, and their main goal is to have Death rule, and fight the living (maybe even kill everyone but that's not 100% clear I think. Death stuff without living souls doesn't work well does it? That's clearly evil, but not chaotic. They are not exactly super reliable though so that speaks against LE. Although some characters probably are.
CG: none. Some Sylvaneth subfaction could fit though.
If the Sylvaneth didn't have the ridiculously evil stuff I'd probably put them here. But they lack the good amount of altruism they would need to be called good I think.
CN: Orruk Warclans (especially Bonesplitterz), Ogres.
They just don't care. They want to roam around and fight and eat. They don't care much about altruism and they don't scheme. They live in the present and just do the thing they do.
CE: Chaos Daemons
The fun problem here is that Warhammer Chaos Daemons are not chaotic by D&D standards. None of the factions is. They all have ordered structures and armies. They are way more akin to the Devils of D&D in that.
I'd still say they are the closest thing to being CE. They don't care for each other nor for the living or death, and they are incredibly evil. They live to destroy literally all there is.
Ok, that's it. I will probably have to refine this post though, I am not yet completely happy.
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Info for the non-D&D guys:
D&D has two main groups of evil outsiders (beings from other planes of existence):
Devils (also called Baatezu)
And Demons (also called Tanar'ri)
Devils are always LE, and Demons are always CE.
Devils are the classic ones that you can deal with, and they have armies and hierarchies and all that stuff. Many of them look like Khorne Daemons.
They want to rule.
D&D Demons on the other hand are more wild, mainly solitary. They do have a bit of a hierarchy but they constantly backstab each other, like Skaven. Like Warhammer Daemons they are manifested feelings.
They want to destroy.
