Despite having relied heavily on Mark's gospel, Luke has even more new material than does
Matthew: stories about Jesus' childhood and influential parables.
Luke did not rely on Mark's Gospel.
Mark and Luke were the names of the scribes who wrote down the Gospel.
Saint Irenaeus Against Heresy Book 3 chapter 1
"Matthew also issued a written Gospel among the Hebrews in their own dialect, while Peter and Paul were preaching at Rome, and laying the foundations of the Church. After their departure, Mark, the disciple and interpreter of Peter, did also hand down to us in writing what had been preached by Peter. Luke also, the companion of Paul, recorded in a book the Gospel preached by him. Afterwards, John, the disciple of the Lord, who also had leaned upon His breast, did himself publish a Gospel during his residence at Ephesus in Asia."
Saint Peter is thus the source of the Gospel according to Mark and Saint Paul is the source of the Gospel according to Luke.