In the Book of Lost Tales, Gothmog was the son of Melkor and an ogress (although it's never said wether the ogress was his wife or not). But this detail was soon removed from the legends.
Similarly, in "Myths Transformed" (HoME, "Morgoth's Ring") Tolkien experimented with a new version for the story of the Sun and Moon, in which Melkor tried to marry the Sun Maia. But this version of the story was never developed or included in the books.
So no, in the final canon, Melkor never had a wife.
As for the Luthien thing, I think the word "lust" is misguiding there. Tolkien never uses that word with a sexual meaning. And if you read the earlier versions of the Silmarillion, as compiled in HoME, from which this passage comes, all of them say that Morgoth plotted some evil against Luthien, but there aren't any hints about him having a romantic/sexual interest in her. Also, the word "lust" doesn't appear in any of the other versions.
So it seems to me that Tolkien simply meant that Morgoth plotted some generic evil plan, but never thought anything specific.
The closest to a "queen" that Melkor ever had would be Sauron, really. XD