Did Paul actually die when he was stoned at Lystra?
Yes, the context concludes that Paul was stoned at Lystra and dragged out as dead. The ancients knew whether life remained, yet the conclusion is that for all practical purposes Saul was put to death by the stoning, making his later standing up miraculous.
Les explains that in Acts 14:19, Jews came from Antioch and Iconium, persuaded the people, and Paul was stoned. According to the Jewish system of execution, they literally felt they had put the man to death, and they drew him out of Lystra supposing he had been dead. Les notes that the ancients were not stupid and had a pretty good idea whether life remained, so he concludes that for all practical purposes Saul was put to death as a result of this stoning. Then verse 20 is miraculous: after an unknown number of hours, with disciples, meaning fellow believers, probably in a dither, Paul suddenly stood up on his feet without any help from an outside source.
And there came thither certain Jews from Antioch and Iconium, who persuaded the people, and, having stoned Paul, drew him out of the city, supposing he had been dead.