But there is no scriptural evidence that he was not a Jew.Paul converted Luke to be a follower of the Messiah.
b'SHEM Yah'shua
And your contention was that through Paul, the Gospel was preached to the Gentiles. Luke was certainly a participant in that as Acts certainly shows.
But there is no scriptural evidence that he was not a Jew.
Many have long believed he was and his Gospel certainly emphasizes the positive attributes of Gentiles (the Good Samaritan).