Could a Jew stone a Gentile under Roman rule?
No. Under the Roman government, a Jew would not have gotten away with stoning a Gentile. Rome allowed the Jews to handle their own religious system and permitted them to execute their own people in the name of their religion, but it never permitted them to stone a Gentile.
Les explains that the stoning of Stephen was a Jewish situation. Under Roman rule, Rome let the Jews pretty much handle their own religious system. The Jews were permitted to kill their own in the name of their own religion, and Rome did not do a thing. Rome never lifted a finger against the Jews carrying out their own means of punishment. Therefore, a Jew stoning a Gentile would not have been tolerated under Roman government; they would never have gotten away with it.