Wenham, John. "Chapter Nine: Ancient Testimony to Luke's Gospel." Redating Matthew, Mark, and Luke: A Fresh Assault on the Synoptic Problem. Downers Grove, Illinois: InterVarsity Press, 1992, 183-197.
Wenham considers early testimony to be unanimous that Luke's Gospel was written by one luke, and normally stated along with an assertion tha this Luke accompanied Paul (Wenham 1992, 184). Some early voices add that Luke is from Syria, that he was a physician, never married, and lived to the age of 84. The Roman custom of putting a tag with an author's name on the outside of a scroll could easily explain the association of Luke's name with the third Gospel (Wenham 1992, 185). Wenham notes a tradition dating to the third century that Luke was one of the seventy sent out by Jesus. Though the tradition is inconclusive, it could explain why Luke spoke at relatively great length about that mission (Wenham 1992, 186).
Where Luke is to be placed in the sequence of the Gospels is a significant matter of debate. According to Eusebius (H.E. 6.14.5), Clement of Alexandria placed the Gospels with genealogies first (Wenham 1992, 188). This led to the "Two Gospel Hypothesis," which took Matthew and Luke to be first. On the other hand, we have Origen, who claims the tradition to be Matthew, Mark, then Luke (Wenham 1992, 189). This tradition, in turn, conflicts with Egyptian codices which are often in the order John, Matthew, Mark, and Luke (Wenham 1992, 190). Irenaeus normally states the order as Matthew, Mark, Luke, and John. This is also the order given in the Muratorian Canon (Wenham 1992, 192). By the fourth century, Wenham finds a solid consensus of the order of composition. Wenham does discuss attempts to reconcile Clement and Eusebius in some detail. He concludes that Mark is best explained as an intermediate step, after Matthew and before Luke (Wenham 1992, 196). The question which remains as of primary importance is whether we should think of the relatinships primarily in literary terms (Wenham 1992, 197).