When Was the Gospel of Luke Written?

Luke's Gospel was likely written around AD 60–61, based on its silence about Jerusalem's destruction, Nero's persecution, and James's martyrdom.
Kevin Zuber

There is no mention of the destruction of Jerusalem by the Romans (AD 70) in either Luke or Acts. If Luke and Acts were written at approximately the same time it probably would have been no later than Paul’s first Roman imprisonment (ca. AD 60–63). The book does not mention the persecution of Nero (AD 64), nor does it mention the martyrdom of James (AD 62). At the outset of his gospel Luke admitted that he used sources (since he himself was not an eyewitness to the events in the gospel). He may have used the Gospel of Mark (written as early as the AD 50s). From these considerations a composition date of AD 60–61 is most likely.