We don't know what exactly happened after he tried to barter for The Throne (or whatever they called it). We do know that he had already had less than the "full measure" of a man's soul. Maybe summoning Shuma-Gorath caused this? At any rate, he came back to the Necropolis and uttered a Black Priest Word of Power (?! they have yet to explain this!!!) to Namor and then he used an incantation from the Blood Bible to summon some Lovecraftian-esque entity that defeated the Great Society.
The bottom line is that Strange cannot be considered "Lawful Good" at this point. He is more or less "lawful neutral," and you could make a similar argument for God Doom.