Was Luke the Evangelist Jewish or Greek?

Last November at the AAR/SBL Annual Meetings I heard a wonderful paper from Matthew Thiessen ("Indices of Ethnicity in Modern Constructions of 'Luke'") that deconstructed my presuppositions regarding the author of the "third" Gospel. I walked away from the session convinced that I could no longer say with confidence that Luke was not a Jew. I was interested to see that this is a question being asked by others. At the "Jewish Studies Blog" Dr. Eli Lizorkin-Eyzenberg wrote an article titled "Could Luke be Jewish, Possibly?" He concludes, "There are no serious reasons to continue to claim that Luke was definitely a Gentile." If "Luke" was Jewish, not Greek, does this change how we read this Gospel?