Two thoughts in response.
The first is a more-or-less scholastic point of AD&D alignment interpretation: in his DMG Gygax says of evil that it "does not concern itself with rights or happiness; purpose is the determinant". So if Sauron is serving something that he conceives of as "the greater good", but detects as evil, then whatever he is serving it is not rights or happiness. What is it, then? And while presumably he agrees it is not rights, does he also agree that it is not happiness? And if he does, what greater good does he think there is in which neither rights nor happiness figure?
Giving the world its God-King? Presumably if you believe such a thing is destined, and Sauron knew much of the the Music of the Ainur, much more than his master, then it may be tempting, if not incumbent on you to bring it about by any means necessary. Sometimes, and I might say frequently, evil people have good reasons to do evil things. That doesn't make them good.
The second point is not about D&D scholasticism but about the LotR. What is Sauron actually doing that could remotely be conceived as contributing to any sort of greater good, however conceived? He is not building any cities. He is not promoting any economic development. He is not even attempting to increase agricultural production. He seems to have no social or economic policies at all. That is why I say that I've always been somewhat puzzled by his motivations. He clearly want to exercise control over people, but doesn't seem to have anything in mind as the purpose for that exercise of control.
What do you think feeds the armies of Southrons and Easterlings that have come from the four corners of the Earth to fight for him? He must be offering them something other than a promised place in the new world order he would establish. I would assume he is already the provider of some sort of stability. Maybe he offered to halt the plagues that were destroying their crops, which, of course, he had created in the first place, if they would only bow down and worship him. Once propitiated, doesn't the renewal of plentiful harvests prove that he
is truly worthy of worship? Unfortunately for this discussion, LR doesn't reveal much about the mind of Sauron. Tolkien, in the novelistic style of LR, doesn't talk about such details. We don't see Aragorn, for example, planning the golden age that was to take place after he assumed the throne, and yet we can see by his actions that he is good. The devices of Sauron, in contrast, tell us he is evil.
J. R. R. Tolkien said:
But at the beginning of the Second Age he was still beautiful to look at, or could still assume a beautiful visible shape – and was not indeed wholly evil, not unless all 'reformers' who want to hurry up with 'reconstruction' and 'reorganization' are wholly evil, even before pride and the lust to exert their will eat them up.
So Sauron was a "reformer", someone who seeks to change the world for the better, it can be assumed. Keep in mind, however, that such a stance can be thought of as sinful, even blasphemous, in the Judeo-Christian tradition, or as hubris in Greek myth. Another purpose for which he may have sought control, and which seems to be at odds with his possible goals as a reformer, might be seen in the making of the Rings of Power. Their most obvious power, even that of the One, was to preserve that which would otherwise have perished from the world. In this work his interests coincided with those of the elves. It could be that the coming Age of Men was something that he saw as a destructive force that he meant to control, or eliminate altogether.
In spite of these goals, however well-meaning, I think that Sauron would have been comfortable self-identifying as evil. He was, after all, a disciple of the original evil. Evil, in this construction of it, accepts domination and oppression as the most expedient and, in fact, necessary means to achieve its goals, however lofty or debased they may be.