Is it true that Lot believed in Abraham after being saved from the fire, and what was Lot's religion before his belief in Abraham?

The exegetes mentioned that Lot believed in Abraham when he was sent as a prophet, and that he had been upon the religion of monotheism before that. The affirmation mentioned here refers to his affirmation of Abraham's miracle when Allah made the fire cool and peaceful for him. That is, he believed in Abraham's message when he saw his miracles, and he was the first to believe in Abraham. As for the principle of monotheism, he was a believer, because disbelief is inconceivable for prophets. It was also said that faith here means a high rank of it.