Lot's sons Moab and Ben-ammi became the fathers of which two peoples?

Answer: Moabites and Ammonites

Lot's older daughter bore Moab, father of the Moabites; the younger bore Ben-ammi, father of the Ammonites.

“The older daughter gave birth to a son and named him Moab. He is the father of the Moabites of today. The younger daughter also gave birth to a son, and she named him Ben-ammi. He is the father of the Ammonites of today.”— Genesis 19:37-38 (BSB)