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There is no contradiction because two things can be true at the same time: 1) Lot sinned in giving his daughters to the crowd of men (Genesis 19:8
Some argue that the Bible is contradictory concerning whether Lot was righteous. 2 Peter 2:7
Genesis 19:8- Behold, I have two daughters who have not known any man. Let me bring them out to you, and do to them as you please. Only do nothing to these men, for they have come under the shelter of my roof.
2 Peter 2:7- ...and if he rescued righteous Lot, greatly distressed by the sensual conduct of the wicked...
There is simply no contradiction between the two passages. A person can be a righteous man, yet commit horrendous sin in his or her life.
Generally speaking, Lot was a righteous man, as 2 Peter 2:7
Likewise, David is described as a righteous man throughout the Bible, yet he committed a horrendous sin in committing adultery with Bathsheba and then causing the death of her husband Uriah.
The fact that a person can be considered righteous despite heinous sin is a testimony of God's grace and forgiveness. Through Jesus' atoning work, one's heinous sins can be completely washed away.
Some people have trouble accepting possible explanations to alleged contradictions in the Bible, especially ones that they consider a stretch. For example, Dan Barker, president of the Freedom From Religion Foundation, says this:
I have received numerous replies from Christians who think that these contradictions are either trivial or easily explained. Yet not a single "explanation" has been convincing.
The fact is that there are plausible explanations for every alleged contradiction in the Bible. That there is a plausible explanation for an alleged contradiction does not mean that it is definitely the correct explanation for the alleged contradiction.
However, as long as a possible explanation has been suggested, then it has been objectively demonstrated that there is no necessary contradiction regarding the Bible verses and passages brought up.
When people like Dan Barker say that they don't find a particular explanation for a contradiction "convincing," then that is merely their opinion. A plausible explanation has been suggested that eliminates the necessary alleged contradiction. They simply don't like it, which is not at all a relevant argument against the explanation.
To read more about solutions to Bible contradictions and difficulties, check out Norman Geisler's The Big Book of Bible Difficulties: Clear and Concise Answers from Genesis to Revelation. While we do not agree with some of Geisler's theology, particularly concerning his view of predestination, this book is still an excellent resource. It is thorough and filled with research.
Another book to check out is Tim Chaffey's Demolishing Supposed Bible Contradictions: Exploring Forty Alleged Contraditions, which also answers many alleged contradictions in the Bible.