Short answer
– The “most likely” author of Luke 19:10 (i.e., the Gospel of Luke) is Luke the physician, a Gentile companion of the Apostle Paul. This is the view held in evangelical circles because of internal clues in Luke‑Acts and early church testimony, and because Luke’s goals and style fit what evangelicals expect of a careful, historically minded Christian writer.

Why evangelicals attribute Luke-Acts to “Luke the physician”
– Early church testimony: Church fathers (e.g., Irenaeus, Tertullian, Clement of Alexandria) identify Luke as the author of the third Gospel and Acts. Evangelicals take this patristic testimony seriously as part of the historical witness to authorship.
– Internal evidence: The Gospel of Luke opens with Luke 1:1–4, where the author describes orderly investigation and use of eyewitness sources. Acts (the book Luke also wrote) contains several first‑person “we” passages (Acts 16, 20, 21, 27) that indicate the author was a companion of Paul—supporting identification with Paul’s companion Luke (cf. Colossians 4:14: “Luke, the beloved physician”).
– Language, style, and method: Luke’s polished Greek, attention to historical detail, and interest in theology and salvation history fit the profile of a thoughtful, educated author—consistent with a Gentile physician who researched eyewitness testimony.
– Theological and pastoral concerns: Luke emphasizes Jesus’ mission to seek and save the lost, compassion for outcasts, and the universal scope of salvation—all themes that appear throughout Luke and Acts and that align with the quote in Luke 19:10.

What evangelicals typically say about Luke (summary of background and emphasis)
– Identity: A Gentile (not one of the Twelve), a physician, and a longtime companion of Paul.
– Works: Author of both the Gospel of Luke and the Acts of the Apostles (Luke‑Acts as a two‑volume work).
– Date: Many evangelical scholars favor a date in the early 60s AD (often before or shortly after Paul’s Roman imprisonment), though some accept slightly later dates; the early‑60s date fits the view that Luke wrote while eyewitnesses were still living and while Acts ends with Paul in Rome.
– Reliability: Evangelicals usually affirm Luke’s careful historiography and theological accuracy, seeing Luke as an orderly historian who relied on eyewitness testimony and oral tradition and who wrote under the inspiration of the Holy Spirit.
– Theological emphasis: Concern for the marginalized, the universality of the gospel (Jews and Gentiles), repentance and forgiveness, and the role of the Holy Spirit and prayer. Luke 19:10 (“For the Son of Man came to seek and to save the lost”) is often cited as summing Luke’s central concern.

Brief note on alternative scholarly views
– Some critical scholars argue for anonymous authorship or date Luke later (80s) and question the identification with Paul’s companion. Evangelicals acknowledge these discussions but generally maintain Luke’s authorship as the most plausible based on the combined internal and external evidence.

Suggested evangelical resources for further reading
– F. F. Bruce, The Acts of the Apostles (and his works on Luke and Acts)
– I. Howard Marshall, The Gospel of Luke (New International Greek Testament Commentary / NICNT)
– Darrell L. Bock, Luke (BECNT)
– NIV Study Bible or ESV Study Bible notes on Luke

Connection to Luke 19:10
– Luke 19:10 encapsulates Luke’s Gospel: Jesus’ mission is to seek and save the lost. Evangelicals see that verse as a concise theological statement of Luke’s portrayal of Christ as the Savior for all people—exactly the emphasis Luke develops in narrative and teaching throughout his Gospel and in Acts.