Why would Saul ask Jesus "Who art thou, Lord?" Did he not know Him as the Lord before his conversion? Also, why did he persecute the church before he was converted?
In Greek, the word most often translated as 'lord' is κύριος (kyrios).
However, by the time of the first century, the vocative form κύριε (kyrie) was also commonly used to address someone with respect, without necessarily implying that they were a 'lord' or 'master' in the sense of a ruler. In modern English, it would be the equivalent of addressing someone as 'sir'.
The Greek text of Acts 9.5 reads as follows, with Paul's question in bold:
Paul addressed Jesus with κύριε. While 'lord' is a possible translation, it is more likely the intended meaning in this case is that of 'sir'. At this point in the narration, Paul doesn't know who it is he is addressing (hence his question), so he plays it safe by using a general title of respect.
Perseus Digital Library, definition of κύριος
Nestle-Aland 28, Greek text of Acts 9
Saul asked God "Who art thou, Lord?" because before his dramatic conversion on the road to Damascus, he did not know the Lord!
As far as I know, God had not spoken to Saul heretofore, so naturally Saul wanted to know who was addressing Him. Wouldn't you? Evidently Saul knew God was the person addressing him, but he needed a bit more information about who this God was! Again, God, we assume, had never spoken to Saul before, except through the Tanakh (the Old Testament Scriptures).
Naturally, God answered Saul's question and told Saul,
Before his conversion, Saul had persecuted the followers of "The Way" (see Acts 9:2; 19:9 and 23; 22:4; 24:14 and 22) because he thought by doing so he was performing God's work. Remember, Saul was a zealous Pharisee who had likely heard about Jesus from other zealous Pharisees who were convinced Jesus had been a fraud and a blasphemer for claiming as he did to be both the Jewish Messiah, and equal to God as well! (Remember Christ's miraculous healing of the man lowered by his friends into the crowded house where Jesus was? What did Jesus say to the man? He said, "Your sins are forgiven." The unbelieving witnesses at that miracle said, rightly, "No one can forgive sins but God alone!").
In retrospect in his letter to the Galatians, chapter one, verses 15 and 16, Paul looks back on his conversion as being the hand of God on his life.
In other words, God had called Paul before he was even born, and then saved him, not only from continuing to persecute, arrest, and imprison followers of The Way, but also to carry and preach the gospel to Gentiles far and near.
Because of his history of persecuting Jesus' followers, Paul felt tremendous remorse after his conversion, and he considered himself to be the least of the apostles and the chief of sinners (see 1 Corinthians 15:9, and 1 Timothy 1:15 KJV). Thanks to God's grace, however, God turned Paul's life around and set him on a path of spiritual fruitfulness in service to Jesus, the one whom he once persecuted! Not only did Paul become a missionary par excellence, but he also wrote a good deal of the New Testament.
Apart from God's grace in his life, Saul would probably have died a bitter old man and no closer to God at the end of his life than he was as a young Pharisee and zealot nearer the beginning of his life, even though he considered himself at the time to be righteous and blameless according to the Law (see Philippians 3:4-6).