Is a woman permitted to seek divorce from her husband whom she rejects due to reasons related to lying, mistreatment, and refusal to have children?

This man did what he should not have done by deceiving his wife, taking her money, and depriving her of her rights. This is not surprising from someone who abandons prayer. The wife should advise him to become righteous, fulfill the rights of Allah, and fulfill her rights, and that he return her money. If he does not respond, she should seek a divorce from him, as there is no good in remaining with a husband who abandons prayer, oppresses her, and consumes her rights.