I think he was a Jewish doctor. It fits with the What advantage then hath the Jew? or what profit is there of circumcision? Much every way: chiefly, because that unto them were committed the oracles of God. principle but if God wanted to choose a Gentile to write the Scripture than he did. He certainly chose the Jews to copy and preserve the OT, as he also chose Gentile Catholics to preserve and copy the NT (as well as the OT) over many centuris. Luke is our brother, our family, whatever his nation was.
Excellent post
Look carefully at Col. 4:11. 14.