Well, first off, they weren't in "the desert". They were in the hills of what is now Lebanon. And, yes, there were men in the vicinity. But there were living men of Sodom and Gomorrah other than their own father.
According to Genesis 19:
"And Lot went up from Zoar and stayed in the mountains and his two daughters with him." Then the first born said to the younger, "Our father is old and there is not a man on earth to come into us after the manner of the earth."
Geographically speaking there were available men just a few miles away. So it may be interpreted that they were looking for something different. The "earth" is often used to denote a fallen unregenerate realm. According to the epistle of James, there is a wisdom from above that is "pure and peaceable," but that there is a wisdom from below which is "earthly, natural and demonic" (James 3:15,17). So you might say that Lot's daughters wanted a man in this "manner of the earth."
As a result of this "earthly" act, both daughters had children. The oldest daughter's son was named Moab. His descendants, the Moabites, were an idolatrous nation practicing ritual child sacrifice. They became one of the primary enemies of the people of Israel.
That sounds like a real stretch. Sounds more to me like Lot wouldn't take his daughters down the mountain to go courtin'.