Although there had been an interest in the message that Paul and Barnabas had preached to them, the people of Lystra in general were easily moved away from it when some Jews came from elsewhere to deal with Paul and Barnabas. Luke does not say how the Jews persuaded the people of Lystra. What he does describe is how the Lord provided evidence that he had been working in the city through Paul and Barnabas.
How would a new and small movement react if their leader was easily removed and left for dead? Normally they would disintegrate and assume that the movement died with him. In Lystra, however, we find that there was a group of disciples who identified themselves with Paul even although he had been left for dead after having been stoned by the Jews.
What did they do as they gathered about him? No doubt, they prayed that he would recover. After all, since the Lord could heal a crippled man there, he could also heal an apostle suffering from the effects of stoning. Whether they prayed or not, the Lord gave to his servant such an incredible recovery that he was able to continue travelling.
We should also note that Paul went back into Lystra first before he left the next day. There could be several reasons for him doing so, but I would suggest that one of them was to show to the citizens that the cruel treatment he had received did not make him afraid. Such a response would have encouraged the new disciples in Lystra as well. His example here is a reminder to leaders that they need to be seen doing what they should be doing for Jesus.
The cruel treatment that Paul had received in Lystra did not affect the determination of Paul and Barnabas to persist in taking the gospel to other places. Opposition should increase our resolve, not stifle it. And because they did so, many were blessed in Derbe, the place they went to next.