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.
Basically, Lot was still in a state of shock thinking about what had just happened. We are reading the happenings like watching TV. Lot was there in person in the midst. He panicked and wanted to play it more safe.
Ellicott gives some more reasons, https://biblehub.com/genesis/19-30.htm
(30) 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.
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.”
16When 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. 17As 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!”
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 foreigner, for the disaster: Why are you the only ones who have survived Sodom and Gomorrah?