I can't agree that the Bible contains actual contradictions. Seeming contradictions - yes, but not actual ones. Those verses which seem to teach free will because they require us to believe or obey don't imply that we have the ability to believe or obey. They show us that we need God's grace if we're to become Christians and lead a God pleasing life, not that we can do so from some imaginary free will. The Scriptures teach that we are dead in unbelief and can't come to Christ in order to be saved unless the Father grants it. (John 6:44,64,65; Eph. 2:1-3 etc.)
With regards to your example of a contradiction -that of Micaiah it's worth quoting the whole passage:
[19] And Micaiah said, Therefore hear the word of the LORD: I saw the LORD sitting on his throne, and all the host of heaven standing beside him on his right hand and on his left; [20] and the LORD said, Who will entice Ahab, that he may go up and fall at Ramoth-gilead? And one said one thing, and another said another. [21] Then a spirit came forward and stood before the LORD, saying, I will entice him. [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. [23] Now therefore behold, the LORD has put a lying spirit in the mouth of all these your prophets; the LORD has declared disaster for you.
(1 Kings 22:19-23 ESV)
So we can see from this passage that Micaiah as God's prophet said truthfully that God had put a lying spirit in the mouth of the king's prophets. So God wasn't lying there. Also who was it that was doing the lying? Was it God or the lying spirits? It was the lying spirits. So God didn't lie. Therefore there's no contradiction. God never lies and He didn't lie in this example that you give.