Lot and his two daughters left Zoar and settled in the mountains, for he was afraid to stay in Zoar. He and his two daughters lived in a cave. One day the older daughter said to the younger, “Our father is old, and there is no man around here to give us children—as is the custom all over the earth. Let’s get our father to drink wine and then sleep with him and preserve our family line through our father.”
That night they got their father to drink wine, and the older daughter went in and slept with him. He was not aware of it when she lay down or when she got up. Genesis 19:30-33
After this, the younger daughter did the same thing. So why would they do this?
First of all, this was not God's plan. The daughters came up with this idea. This was a sinful idea that the Bible merely reports but does not support.
So why would they do this? First of all, they were virgins, promised to be married, but their fiances died in the Sodom and Gomorrah destruction.
They wanted a family but here they were, stuck in a cave, afraid to move and wondering what their future would hold. They had just seen their entire world destroyed and were probably a little anxious. "Is everyone dead? Are we next?"
With no other man around, they figured, let's use dad to "preserve our family line." The lesson from Sodom and Gomorrah was "Don't mix with bad people!" so they wanted to keep this within their own family, not to leave the cave and find just anybody.
Fearing the only man they knew could die, they took action. It doesn't appear they did this because they loved him in a romantic way, but only as a provider of an X or Y chromosome.
Their instincts proved fatal. The two sons born of this encounter - Moab and Ben-Ammi - were the patriarchs of the Moabites and Ammonites, two of Israel's biggest enemies that they fought against all throughout the Old Testament.
God did not bless this encounter. He could have provided the right husbands for them if they only waited.