Another interesting early tradition about Luke is that he (Luke) is “the brother, whose praise is in the gospel throughout all the churches” of 2 Corinthians 8:18. Many take this to suggest Paul is referring to Luke’s already-written gospel. The gospel was evidently written while Paul was still alive, since Luke wrote his gospel before he wrote the book of Acts (Acts 1:1), so prior to AD 62 (in my opinion).
John Chrysostom (circa AD 347-407) says this in Homily 10 on the Second Timothy:
“Only Luke is with me.” For he adhered to him inseparably. It was he who wrote the Gospel, and the General Acts; he was devoted to labors, and to learning, and a man of fortitude; of him Paul writes, “whose praise is in the Gospel throughout all the Churches.” 2 Corinthians 8:18Jerome of Stridon in De Viris Illustribus (On Illustrious Men) Chapter 7 (circa AD 345-420) says Luke:
wrote a Gospel, concerning which the same Paul says, “We send with him a brother whose praise in the gospel is among all the churches”And in Letter 53, To Paulinus
...once we realize that their author is Luke the physician whose praise is in the gospel...The longer recension of the Epistle of Ignatius of Antioch to the Ephesians (Chapter 15) (died circa AD 108-140) credits Luke as being this brother whose praise in in the Gospel.
For he who shall both “do and teach, the same shall be great in the kingdom.” Our Lord and God, Jesus Christ, the Son of the living God, first did and then taught, as Luke testifies, “whose praise is in the Gospel through all the Churches.”Eusebius of Caesarea (circa AD 262–3390) in Church History, Book III.4.8 makes a reference that seems to say Luke’s Gospel was already written when Paul was writing (though he doesn’t mention the 2 Corinthians passage).
And they say that Paul meant to refer to Luke’s Gospel wherever, as if speaking of some gospel of his own, he used the words, according to my Gospel.Some conservative scholars believe that AD 55-57 is a “reasonable estimate” for dating 2 Corinthians. If so, it would not be far of the possible dating of AD 58-59 that some give the gospel of Luke. Nevertheless, the interpretation of Luke being “the brother whose praise is in the gospel” is tenuous enough that one would not want to be too dogmatic about it.