Lot was AFRAID to stay in Zoar; so he lived in a cave with his two daughters

Genesis 19:

30 Now Lot went up out of Zoar and settled in the hills with his two daughters, for he was afraid to stay in Zoar; so he lived in a cave with his two daughters."

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Why was Lot afraid? He didn't do anything.

Genesis 19:

23 By the time Lot reached Zoar, the sun had risen over the land. 24Then the Lord rained down burning sulfur on Sodom and Gomorrah—from the Lord out of the heavens. 25Thus he overthrew those cities and the entire plain, destroying all those living in the cities—and also the vegetation in the land. 26But Lot’s wife looked back, and she became a pillar of salt.

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Lot was in a state of shock, thinking about what had just happened. We read about the happenings like we were watching a movie, but Lot was there in person. He panicked and wanted to play it more safe.

Ellicott gave some more reasons:

He feared to dwell in Zoar.--Though this little place had been granted him for an asylum, yet, terrified at the sight of the smoking valley, and remembering that he had been originally commanded to go to the mountains, he summons up his courage and proceeds thither. The limestone regions of Palestine are full of caverns; and the patriarch, whose wealth had been so great that he and Abraham could not dwell together, is now content to seek in one of these caverns a miserable home.

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Lot was scared. Very few people wouldn't be.

Genesis 19:

15 With the coming of dawn, the angels urged Lot, saying, “Hurry! Take your wife and your two daughters who are here, or you will be swept away when the city is punished.”
16 When he hesitated, the men grasped his hand and the hands of his wife and of his two daughters and led them safely out of the city, for the Lord was merciful to them. 17 As soon as they had brought them out, one of them said, “Flee for your lives! Don’t look back, and don’t stop anywhere in the plain! Flee to the mountains or you will be swept away!”

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Put yourself in his shoes. You may do the same just in case of whatever. The people of Zoar may blame you and your daughters, the foreigners, for the disaster: Why are you the only ones who have survived Sodom and Gomorrah?

See also Why Lot wanted to flee to Zoar instead of the mountains as the angel instructed?