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There is a difference between sending a lying spirit and actually lying. Even though God is sovereign over sending the lying spirit, He is not the one doing the actual lying. It is the spirit who is committing the lie and committing the sin. God is not guilty of lying or sinning. So, there is no contradiction for God to send a lying spirit.
Some say that the Bible is contradictory concerning God sending a lying spirit, since God is a righteous God who cannot lie. Here are the relevant verses:
1 Kings 22:22- And the Lord said to him, ‘By what means?’ And he said, ‘I will go out, and will be a lying spirit in the mouth of all his prophets.’ And he said, ‘You are to entice him, and you shall succeed; go out and do so.’
Titus 1:2- in hope of eternal life, which God, who never lies, promised before the ages began
There is simply no contradiction at all between these two verses. If 1 Kings 22:22
There is a difference between being sovereign over sending a lying spirit and actually lying. God has not revealed a law where it would be wrong for Him to send a lying spirit.
Similarly, even though God has decreed, and is sovereign over, sin, that does not mean God is guilty of sin, or that He has committed any sin. The person who actually commits the sin is the one who is guilty of the sin.
A comparable Scripture passage is Acts 4:27-28
27 for truly in this city there were gathered together against your holy servant Jesus, whom you anointed, both Herod and Pontius Pilate, along with the Gentiles and the peoples of Israel, 28 to do whatever your hand and your plan had predestined to take place.
This passage does not even say that God sent a spirit to cause Herod, Pontius Pilate, the Gentiles, and the peoples of Israel to crucify Jesus. It says that God himself predestined the death of Jesus through these people.
The reason why God is not guilty of sin in all of this is that it is simply not wrong for God to decree and be sovereign over sin because He is not the one who is actually committing the sin. It was Herod, Pontius Pilate, the Gentiles, and the peoples of Israel who actually committed and were guilty of sin.
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.