In the Middle Ages, Luke emerges as the patron saint of artists and painters. A 14th century writer, Nicephoros Kallistos, attributed to a 6th century Byzantine, Theodoros Anagnostes, the memory that “an image of the Mother of God [was] painted by the apostle Luke.”
The portraits, as attributed to Luke, portray him painting the Virgin Mary. “Precisely why Luke is remember as patron of artists is unknown.” Although an original painting no longer remains, an ancient picture has been brought to the Church of Santa Maria Maggiore in Rome following the conquering of Constantinople in the 4th crusade. All subsequent images of Luke as painter portray him painting the Virgin Mary.
For more on this tradition, see: M.Parsons, “Who Wrote the Gospel of Luke?” BRev 17, no. 2 (2001): 12–20. Sean P. Kealy, The Interpretation of the Gospel of Luke, vol 1. of From Apostolic Times throughout he Nineteenth Century, SBEC 63. Lewiston: Edwin Mellen Press, 2005.
Also, here are a number of alleged paintings and locations: see here.
 Edwards, Luke, 11.