Short answer: Most evangelicals attribute Luke 2:11–14 (and the whole Gospel of Luke) to Luke the physician, a Gentile companion of the apostle Paul who also wrote Acts. He is viewed as a careful, educated historian and a friend/partner of Paul who wrote to give an orderly, eyewitness-based account of Jesus and the spread of the early church.

Why Luke is identified as the author (evangelical summary)
– New Testament references: Paul names Luke among his coworkers (Colossians 4:14 calls him “the beloved physician”; Philemon 1:24 lists him with fellow workers).
– “We” passages in Acts: Several sections of Acts switch to first-person plural (e.g., Acts 16:10–17; 20:5–21:18; 27:1–28:16), which many evangelicals take as indicating the author was a traveling companion of Paul and an eyewitness of those events.
– Early church testimony: Early Christian writers (e.g., Irenaeus, Tertullian, Clement of Alexandria) attribute the Gospel and Acts to Luke.
– Literary and theological unity: Luke and Acts form a two-volume work with consistent style, vocabulary, and themes (care for the marginalized, universal scope of salvation, role of the Holy Spirit, concern for historical detail), which supports common authorship.

What evangelicals typically say about Luke (biographical and pastoral profile)
– Background: Likely a Gentile and not one of the twelve apostles; often described as a physician (the Greek term iatros in Colossians). Evangelicals usually accept the plain reading that he was a medically trained person and a friend of Paul.
– Education and style: Luke is thought to be well-educated and a polished Greek writer—his Gospel is the most orderly and historically oriented of the four, opening with the claim that he carefully investigated eyewitness testimony (Luke 1:1–4).
– Dates: Many evangelical scholars date Luke-Acts in the 50s–60s AD (commonly the early 60s), sometimes before Paul’s death, though there is range among scholars.
– Theological emphases: Luke highlights Jesus as Savior for all people (Jews and Gentiles), compassion for the poor and outcast, fulfillment of Old Testament promises (line of David, prophecy), and the outworking of God’s plan through the Holy Spirit. These emphases are evident throughout Luke and in passages like Luke 2:11–14.

How that relates to Luke 2:11–14
– The angels’ proclamation—“Today in the city of David a Savior has been born to you; he is Christ the Lord”—fits Luke’s emphases: historical grounding (Bethlehem, “city of David”), messianic identity (Christ), and universal salvation (the title “Savior” and the angelic proclamation reaching ordinary shepherds).
– “Glory to God in the highest, and on earth peace to those on whom his favor rests” reflects Luke’s themes of God’s glory, peace with God, and God’s mercy toward the humble and marginalized—consistent with his concern for the poor, the lowly, and the inclusion of all nations.

Suggested evangelical resources if you want to read more
– Darrell L. Bock, The Gospel of Luke (BECNT)
– I. Howard Marshall, The Gospel of Luke (NIGTC)
– F. F. Bruce, The Gospel of Luke (Tyndale)
– N. T. Wright, Luke for Everyone (more accessible/ pastoral)

If you’d like, I can give a short biographical sketch suitable for a church handout, a bibliography of academic evangelical treatments of Luke, or a brief exegesis of Luke 2:11–14 from a conservative evangelical viewpoint. Which would you prefer?