Above all the ultimate, true source behind Luke's gospel was the Holy Spirit--the Spirit of truth who taught his inspired penmen all things and brought to remembrance all that Jesus had said (John 14:16,17,26). The Spirit's inspiration of his penman does not rule out the writer's use of material at his disposal to document under the Spirit's guidance what he was writing. In using those materials the Spirit's guidance would have led the writer to leave out any chaff of error and to preserve only the wheat of what was the truth.
Paul was a source for Luke's gospel. As stated in the section about Luke the writer, Luke was a companion and assistant of the apostle Paul, who had seen Jesus and had been instructed by Jesus. Luke thus learned from Paul the gospel of Jesus Christ that Paul preached in his missionary endeavors.
Mark was another potential source of information for Luke. Luke associated with the gospel writer Mark. Luke first met Mark in the church of Antioch, where Luke was a member and where Barnabas and Paul had brought Mark in A.D. 44 to assist them (cf. Acts 12:25). Luke was also with Mark, as well as with Paul, in Rome during Paul's first imprisonment there and when Paul wrote his prison epistles, (cf. Colossians 4:10,14; Philemon 24). Luke and Mark were again together with Paul in Rome during Paul's second Roman imprisonment before his martyrdom (cf. 2 Timothy 4:10,11). Mark had heard and learned the gospel that Peter had preached (cf. An Overview Of The Gospel Of Mark). It is thought that since Luke was in Rome with Mark during both of Paul's Roman imprisonments, and since Mark wrote his gospel in Rome in the mid A.D. 60's, Luke is likely to have obtained a copy of Mark's gospel very soon after it was written and followed it in the course of writing his own gospel.
Peter himself, whose preaching was the basis of Mark's gospel, may have been a source of information for Luke in preparing his gospel. Luke's whereabouts between Paul's first and second Roman imprisonments in A.D. 61 to 62 and in A.D. 67 is unknown. If Luke remained in Rome for those five years or so, he is likely to have had contact with Peter. Peter was in Rome and there wrote his first letter around A.D. 62 to 64 and his second letter around A.D. 66 to 67. Assuming Luke remained in Rome during those years, he had the opportunity to hear from Peter the gospel of Jesus that Peter preached.
Luke traveled with Paul to carry the collection of the Gentile churches to the poor Christians in Jerusalem. While there Luke met James the brother of the Lord Jesus and the elders of the church, (cf. Acts 21:18). He would also have had the opportunity to interview the apostles who were in Jerusalem, plus the many other Christians who had witnessed Jesus' teachings, miracles, suffering, death, and resurrection. There were many such Christians, for Paul noted in 1 Corinthians 15:6 that Jesus had appeared after his resurrection to more than five hundred such disciples at one time, many of whom were still living. Luke also spent the two years of Paul's imprisonment in Caesarea near Galilee and Judea. It would have been a simple matter for him to travel those areas where Jesus had conducted his ministry and talk with the eyewitnesses.
I found those facts so interesting (If you click on Luke this will take you to the website) I have not got much more time tonight as I need to get on with some work. Have a blessed evening or day depending which side of the planet you live!
Picture: Luke, 1360–64 Attributed to Master Theodoric, Prague