The Gospel of Luke was written some 40 to 70 years after the ministry of Jesus and then not widely distributed for another hundred years. It was fed by the Oral Teachings of the Apostles and witnesses which continues to this day.
First of all, by all accounts Luke was written from 58-63AD so thats only 25 30 years so that 40-70 years is in error. Second, how soon it was widely distributed is immaterial to this discussion. The point is that he saw a need to write things down because already by that time oral transmission was obviously causing problems.
>>It was fed by the Oral Teachings of the Apostles and witnesses which continues to this day.<<
Seriously? They have convinced you that the apostles and witnesses are still alive today? Go figure.