Why did God send a lying spirit if God cannot lie?

1 Kings 22:22 and Titus 1:2

God sends a lying spirit (1 Kings 22:22) - “And the Lord said to him, ‘How?’ And he said, ‘I will go out and be a deceiving spirit in the mouth of all his prophets.’ Then He said, ‘You are to entice him and also prevail. Go and do so.'"
God cannot lie (Titus 1:2) - "in the hope of eternal life, which God, who cannot lie, promised long ages ago."

This is an anthropomorphized account of a spiritual reality. In other words, it is a human representation of what happened in the spiritual realm. If you take a look at the text you can see that God is asking questions.

v. 20 “The Lord said, ‘Who will entice Ahab to go up and fall at Ramoth-gilead?’ And one said this while another said that.
v. 21 “Then a spirit came forward and stood before the Lord and said, ‘I will entice him.’
v. 22 “The Lord said to him, ‘How?’ And he said, ‘I will go out and be a deceiving spirit in the mouth of all his prophets.’ Then He said, ‘You are to entice him and also prevail. Go and do so.’
v. 23 “Now therefore, behold, the Lord has put a deceiving spirit in the mouth of all these your prophets; and the Lord has proclaimed disaster against you."

Did God need to ask questions so as to learn? Was he trying to figure out what was going to happen? Of course not. Since God knows all things (1 John 3:20) and he has ordained whatsoever shall come to pass (Ephesians 1:11), he already knew who would step forward to do the deceiving. God was carrying out the sovereign plan that he had predestined to occur; in this case, the destruction of Ahab by the use of his own false prophets. Consider this...

"For truly in this city there were gathered together against Your holy servant Jesus, whom You did anoint, both Herod and Pontius Pilate, along with the Gentiles and the peoples of Israel, 28 to do whatever Your hand and Your purpose predestined to occur," (Acts 4:27-28).

God predestined the death of Jesus at the hands of Herod, Pilate, the Gentiles, and the Jews. Yet God was not the one who forced them to sin. When we say that God ordains, or that he predestines something bad to happen, we're saying that he is allowing it to happen by his sovereign will. We call this his permissive will. It is his will to permit it, because it is part of his greater plan. He plans to permit it. He could alter it, but he decides not to do so.

Likewise, in 1 Kings 22:22, God was revealing to us the reality of the spiritual realm, though in human terms, of His ordained sovereign plan by which Ahab would be destroyed by the counsel of his false prophets.

Does this mean that God who sent a deceiving spirit is a deceiver himself?

No, God sending a deceiving spirit does not mean that he is a deceiver. He was merely sending a demonic force, allowing it to perform what was natural to it, to do something that was part of the greater plan of God. If I send my wife to the store to get something, I am not the one doing it -- she is. If I know that in the process she is going to speed and break the law, am I the one guilty for her speeding? Of course not, since she is exercising her free choice.