For quite some time I have been puzzling over the commonly accepted belief that Luke was a gentile. I have found the gospel of Luke to be one of the most Hebraic books in the New Testament, both in its very Hebraic forms in the Greek language and in its content. (Some years ago I wrote a series of blog posts on Hebraisms in New Testament Greek— The Hebraic New Testament.)
Dr. Lizorkin-Eyzenberg does a nice job of questioning the common assumption that Luke was a Gentile; his discusses this question in his blog post Could Luke be Jewish, Possibly?. He points out that most of the arguments for Luke's non-Jewishness are insubstantial. The only argument that has any merit is the one taken from Colossians 4:7-18. I won't repeat Dr. Lizorkin-Eyzenberg's points, but here is his summary on the Colossians text.
In other words, the argument that says that this separate mention clearly sets Luke apart from Paul’s kinsmen is unsound, simply because it tries to extract too much mileage from this text. It cannot prove what it sets out to prove. It only allows it as one possible reading of this textual unit.
The idea that was totally new to me was the possibility that Luke is the same person as Lucius mentioned in Romans 16:21.
“Timothy, my co-worker, greets you; so do Lucius and Jason and Sosipater, my relatives.”
(Romans 16:21 NRSV)
Dr. Lizorkin-Eyzenberg concludes by leaving the question without a definite answer— we simply can't prove for certain whether Luke was Jewish or not. But he clearly is open to the possibility that Luke was Jewish.
There are no serious reasons to continue to claim that Luke was definitely a Gentile. So to answer the question I asked in the title of this essay: “Can Luke be Jewish possibly?” The answer has to be given in affirmative.