Upon arrival to the land of Zoar Lot preferred to shelter in the mountains. It's obvious that Lot was afraid to dwell in any cities near Sodom as the destruction of the city was horrendous. He arrived there with his daughters only because his sons in law rejected the message that the city was going to be destroyed and his wife couldn't seem to separate herself from the city and eventually became part of what was left of the city.
Lot's daughters thought that their father and they were the only people left on the planet. This is probably because the city of Sodom exploded and they had no way of telling if everyone on the earth had perished or not. The angels of course did not tell them this so they just took it upon their feelings and emotions to continue the sinful lifestyle of Sodom rather than trusting in the Lord.
Now, this is where it gets scary, Lot's daughters got Lot drunk with wine to propagate the seed. Many would think that Lot is an upright and righteous man when in fact I have a different opinion. First of all Lot, when he separated from Abraham, went to Sodom to become a rich and powerful man in this sinful city. Then we read in the bible that he offers his daughters to a mob of demented sexual freaks in the street to have their way with. Then his wife which should be a reflection of his righteousness doesn't want to leave the city as they are directly by an angel to leave town. Then he gets drunk two nights in a row like nothing happened after probably millions of people died in the city of Sodom, which was less than a days walk from where he was and he is so drunk that he doesn't remember his daughters the next day? Really?
Although he is described as being righteous in 2 Peter 2:7-8 I think that the only way I can see this is if he became righteous after the fact, although it's not up to me to judge others in this way because the bible tells us that there are none that are worthy Romans 3:10.
I also should also add it's also suggested that these daughters were actually daughter in laws and not his actual daughters by bible hub. Scroll down half way until you see the pulpit commentary for Genesis 19:30. I have problems with it but I do want to add other opinions if available.
It's my opinion he was so promiscuous and was with so many different women that he didn't even recognize his own daughters. Not exactly what one would have in mind when they think of righteous people.
This passage also tells us the origin of the Moabite and the Ammonite nations.