Lot and his daughters camp out in a cave for a while. The daughters get their “just and righteous” father drunk, and have sexual intercourse with him, and each conceives and bears a son (wouldn’t you know it!). Just another wholesome family values Bible story. (19:30-38)
Respond: Before the destruction of Sodom and Gomorah, Lot speaks to his future son-in-laws who were to marry his daughters, but his son-in-laws thought he was joking (Gen 19:14). We see here that Lot had arranged son-in-laws for his daughters, but since they took the instruction of Lot lightly they could had perished from the wrath of Yahweh God. Daughters slept with their father (Gen 19:30-38) is not new similar case of incest is noticed when Caine takes a wife unto himself in (Gen 4:17). The Bible never encourages us to do so but these are just records, and one must not forget that these things happened before the law was given. Now it was the daughters of Lot that made him drink a) It was the daughters who did so and Lot was innocent and b) When the daughters slept with their father, Lot was intoxicated by wine and he was not in his senses of the act.
So, the above situations proves that Lot was just and righteous (2 Pet 2:7-8). Reason for such act is Lot’s daughters feared that there was not a single man in Zoar with whom they can consummate and have children. So, Bible has the answers only we need to read the verses before and after.