What does Genesis 19:34 mean?
Lot's daughters are reeling from the loss of their home, mother, and prospective husbands during the annihilation of Sodom. Apparently, they have no sense of trust in God, or His provision for their future. Instead, they seem convinced they no longer have any hope of marriage or children. This faithlessness is not unexpected, since Lot chose to plant his family deeply in the midst of a godless, depraved Sodomite culture.The plan these women devise to fix their predicament is also reflective of the culture in which they were raised. Earlier, men of the city demanded two strangers be sent out of Lot's home in order to be raped (Genesis 19:5). Recently, Lot's daughters have plotted to conceive children by sexually violating their father—getting him drunk to the point of stupor and then having sex with him.
Lot's oldest daughter has already been successful in her attempt. Since her scheme worked on the previous night, she encourages her younger sister to take advantage of their father, as well.