"Luke is an interesting writer because he did not know Jesus Christ personally.
He became a follower after the Lord’s death, when Paul taught him the gospel.
Luke had been a physician, but he left that profession to travel with Paul. He
had the opportunity to talk with many of the Apostles as well as others who were
eyewitnesses to special events or moments in the Lord’s life. In the first few
verses of his book, Luke says that he is going to write the things that
eyewitnesses and other teachers of the gospel had to say about the Savior.
Apparently he had the opportunity to talk to many who were present when the
Savior taught or performed miracles.
One of the most amazing stories Luke wrote about was the birth of the Savior. Elder Bruce R. McConkie (1915–85) of the Quorum of the Twelve Apostles says that Luke probably got his
information about Jesus’s birth from Mary herself. Who were the other people Luke interviewed about Jesus Christ? The list would have been long. Many of the people who knew the Savior would still have been alive and would have remembered such important times in
their lives. Paul mentions that about 500 people saw the Savior after His Resurrection and that most of them were still alive when he was writing to the Corinthians (see
1 Corinthians 15:6). "
from the New Era, Who Were Matthew, Mark, Luke, and John? by Janet Thomas (pp 20-21)