Are Stories About Prophet Dawud (AS) and Prophet Lut (AS) in the Bible Authentic?

After the revelation of the Qur’an, the only fully preserved and reliable book of guidance is the Qur’an itself. Therefore, an ordinary Muslim does not need to study the Bible or previous scriptures in order to learn faith and religion. The earlier scriptures were originally revealed by Allah, but many changes and distortions have occurred in them over time, so distinguishing truth from falsehood is not something every person can safely do.

As for the incidents you mentioned  such as the accusation that Prophet Dawud (David), peace be upon him, committed adultery and arranged a killing, or the story about Prophet Lut (Lot), peace be upon him, and his daughters these are false and fabricated claims that are against the honor and dignity of the Prophets. In Islam, the Prophets are chosen and purified servants of Allah, and the Qur’an and authentic Islamic teachings reject such accusations.