Was Saint John the Evangelist a martyr?

No. Luke was an occasional companion of Paul. Colossians 4:12-14 tells us that he was a physician, but this information should be used with caution, as a majority of New Testament scholars say that Colossians was not really written by Paul, but was written pseudepigraphically in the 70s of the first century - probably by someone who had never met Luke.

We know from Paul that St. Luke was a Christian, but we do not know how much he knew and understood about Jesus. The gospel that now bears his name was originally anonymous and was only attributed to Luke by the Church Fathers later in the second century.