When the Reformation began to take hold, the Orthodox may have been in decline, but were definately still present. I'm curious to know what what the two "breakaways" thought of each other - is it a case of "my enemies' enemy is my friend," or was the doctrinal difference too great?
I linked to this article in another question, but it's certainly relevant here:
Some Lutherans did make contact with Patriarch Jeremias II of Constantinople. They gave him a copy of the Augsburg Confession and requested his reaction. The Patriarch politely thanked them and, later, gave a detailed reply, indicating where the various points of the Lutheran document were in conflict with Orthodox doctrine.
The Reformers, in turn, composed a detailed reply to explain themselves and assert that doctrinally the two churches were not really so far apart. The Patriarch replied at greater length, again explaining which doctrines were not acceptable to the Orthodox faith.
The Reformers sent one more letter, but the Patriarch felt things were at an impasse. He replied requesting no more correspondence on matters of doctrine, but rather "for the sake of friendship."
It is doubtful that, considering the pressures every hour placed on Martin Luther at the time, he gave a great deal of thought to the Eastern Orthodox. If so, it surely would have been left in his abundant writings, of which we have volumes. Communication between Orthodox and the Roman Catholic West, were limited at best. this was about the same era as the Fall of Constantinople to the Turks, so I doubt greatly that the Orthodox Divines were much concerned about the stir of a lone Augustinian Monk in Germany.
Orthodoxy has never been a "breakaway" from anything. It is the original church. Rome broke away from Orthodoxy to become a secular power in Western Europe. Luther was viewed by Orthodoxy as under a straying bishop of Rome, and the Patriarch Jeremiah II in the 17th century advised Luther's followers to address their complaints to the bishop of Rome first, and first reconcile their ojections with him. The Orthodox Church except for Russia was under the Ottoman yoke in the east and under Roman domination in the west. A humdred years before Luther, Jan Hus of Czechia (Bohemia) intended to remain Orthodox, but was burned at the stake for this by Rome in the 14th century. The martyred St. Jan is now an Orthodox saint. (Czechia is the land of another saint Good King Wenceslaus.)
Luther's influence from the Blessed Augustine was too great for him to absorb the depth of the Orthodox view of the Trinity in which the Son is begotten of the Father and the Spirit "proceeds from" the Father, hence Luther's aversion to relinquishing the Roman unilateral and arbitrary addition to the canonical formulation of the Creed of Symbol of Faith approved over a thousand years earlier at the Council of Nicaea, a western addition known as the filioque or "and the Son", which had its first appearance in a Spanish priest's rendition of the Creed. While there are New Testament bases for both views, only the Orthodox view is supported by the whole Tradition of the Church from its beginnings. The Roman wording is a new encrustation without the test of Tradition as given to us by the unbroken chain of tradition from the early church.
Luther probably had too much on his political plate to think too much about his fellow Christians in the East. They were too far away to help him anyway.