I don't think it was Luther but some Lutherans at the University of Tübingen who corresponded with Patriarch Jeremias II of Constantinople in the late 1500s. Lutheranism retains enough in common with Roman Catholicism and Orthodoxy to make that dialogue feasible; not so the full-on Calvinists (Puritans, Presbyterians and Reformed) who AFAIK never tried to have one. But the Lutherans were trying to start a relatively mild 'Reformation' among the Greeks rather like in the Scandinavian countries. It didn't work.
To see what the Lutherans might have wanted the Orthodox to become check out the Ukrainian Lutheran Church
, IIRC a 1930s split from the Greek Catholics. Lutherans have no problem with vestments, icons (as teaching aids not for veneration) and three-bar crosses (Lutherans have always used the crucifix) so there you go.
There were no mass moves eastward during the 'Reformation'; that came later, in the 1900s, from a few little groups of ex-RCs who joined the Russians (vagantes
, not from the Old Catholic Church, an 1870s schism from Rome now liberal).
(Also, in the 1800s some Portuguese ex-RCs in India joined the Syrian Church over internal fights not really to do with theology.)
And yes, the Synod of Jerusalem and Confession of Dositheus were against Calvinism after another patriarch of Constantinople, Cyril Lukaris, converted to Calvinist beliefs and tried to inflict them on Orthodoxy (rather like Jansenism in the Roman Church?).