Did Mark and Luke actually walk with Jesus?

Mark was the son of Mary of Jerusalem (not the mother of Jesus) and Luke was a gentile physician. Neither were among Jesus disciples, although it is considered that the reference in the Gospel of Mark to a young man who ran away naked from Gethsemane when Jesus was arrested, is an oblique reference by Mark to himself.

In any case both of these Gospel writers had reliable sources close to the events they described and so, even though they were undoubtedly Christians, their sources did not include Jesus Himself but His followers.