Saint Luke was a monk at the Deep Stream (Βαθέος Ρύακος) Monastery near Triglia, Lykaonia (in Asia Minor), and later became its third Igoumen, He reposed there in peace at the end of the X century.
The Monastery, dedicated to the Transfiguration of Christ. was famed for the strictness of the ascetic life of its monks. The first Igoumen and founder of the monastery was Saint Basil (July 1), and the second was Saint Ignatius (+ September 27, 970).1
According to the Hagiologion of Metropolitan Sophronios Eustratiadou, Saint Luke is commemorated on September 7. Only Saint Nikodemos of the Holy Mountain (July 14) lists his commemoration on December 27.
1 Some sources list Saint Peter (September 7) as the second Igoumen.