The Eastern Orthodox being Christians also believes in the teaching of saint Paul on the subject, but they have a different theology than Lutheranism. Probably the Best way to answer your question (without spending tons of time researching it) is to point you to an article that covers the correspondence made between Lutheran theologians and an Eastern Orthodox Patriarch that took place a few decades after the death of Martin Luther.
Justification by Faith Alone?
The Reply of Patriarch Jeremiah II to the Lutheran Tübingen Theologians, Concerning the Augsburg Confession (16th cent.)
"... The same also do the ancient writers of the Church teach; for Ambrose saith: 'This is ordained of God, that he that believeth in Christ shall be saved, without works, by faith alone, freely receiving remission of sins." —Article VI of the Augsburg Confession
Here is another article that covers the basic areas of Agreement and disagreement between Lutherans and the Eastern Orthodox in regards to that early contact by the Tubingen theologians.