Lystra is the city where Paul was stoned by the adversarial Jews. Afterward, he somehow got up and walked away. Then, after preaching in Derbe, the Bible says, 'They returned to Lystra, Iconium, and Antioch, strengthening the souls of the disciples, exhorting them to continue in the faith, and saying, 'We must through many tribulations enter the kingdom of God.' So when they had appointed elders in every church, and prayed with fasting, they commended them to the Lord in whom they had believed' (Acts 14:21-24).
To answer your question, Paul responded to the persecution in Lystra by going back into the city, strenthening the believers, appointing elders to oversee the church, and commending them to the Lord. This is all the Bible tells us about Paul's response to the persecution in Lystra.
We would also note how Paul encouraged the people to continue in the faith: 'We must through many tribulations enter the kingdom of God.' His stoning was an obvious example of the kind of tribulations he had in mind. Paul clearly practiced what he preached.