I think we have to consider which version of 40K's GE we're discussing here. The 1980s and 1990s version was pretty clearly LE by D&D standards, because he required constant human sacrifices (literally constant - sometimes a conveyor belt was involved - it seems like many or all, depending on source, were unwilling, too) to maintain his power, and his agents, working in his name, and with his full apparent divine support, would do things like murder planets with billions of human inhabitants, often on somewhat flimsy reasoning.
He's far beyond any line which could reasonably be considered LN, because sheer enormity of the acts of genocide and mass destruction committed directly in his name makes the greatest devils of D&D look like friendly puppies by comparison. Asmodeus would blanch at some of that stuff, even.
Yet it is all to a very specific order and purpose - so clearly he's Lawful.
More recently, some depictions have attempted to tone this down, with stuff like him requiring far fewer or no human sacrifices (again depending on source), or them all being willing sacrifices, and Exterminatus and the like being used far more cautiously and with a lot more hand-wringing, and you might, if you took the most generous possible take on all of those, get to LN. It's all a bit of a giant retcon and still inconsistent, though.
But it's the Blood War, essentially. LE vs CE, because Chaos is most assuredly CE. LN would be more like the Tau, who are not involved in the same kind of genocide and mass-murder as a matter of course (whereas it is literally how the Emperor and his empire work), but do some incredibly creepy things in the name of order (mass sterilization of humans in their space, for example).
Literally no currently existing faction in 40K could be seen as Good in the D&D sense, I'd argue. You might have been able to have Squats as LG when they were still around, but no more. Individuals can be, of course.
I would agree with your general point that the Emperor started LG, then became LN out of necessity, but in many/most portrayals, I would say he is clearly LE. This is the result of the extreme actions he's had to take to stay "alive" and to fight Chaos, sure, but it's clearly that he's been brought down to the level of Chaos, despite better intentions. Without such powerful adversaries, he'd probably go back to being LG, as you say.