“If I may respectfully ask, in what sense do the Orthodox pray for the souls of the departed? As you know, this is not a practice within Protestantism.”
You ask in what sense do we pray for the souls of the departed. Why, in the same sense that we pray for the souls of those with us because Christ is Risen, trampling down death by death. The barrier between living and dead has been eliminated due to the Resurrection of Christ. Those who are departed are just as much with us and just as much a part of the Church as those who we see living on this earth. There is no longer any separation. And so not only do we pray for them, but they also pray for us; in the same way that you might ask your friends to pray for you and in turn pray for them so also do we pray for each other without concern for the separation of death.
When we pray for either the living or the dead we use the same prayer: “Lord have mercy”, to express our desires. We do not know what to pray for even for those with whom we live because only God knows what is best for our salvation, and so we say “Lord have mercy”. Likewise we do not know the needs and concerns of the departed, but God does and trusting in His knowledge we say, “Lord have mercy”
We do know that, like all of us, those who have departed require forgiveness of sins, and that they look for a “place of rest” in the bosom of Christ and so we make this petition, that God will provide these things, but again as for specifics about how this should happen we simply conclude with “Lord have mercy”.
Some of the confusion might occur in that most Protestant confessions teach that the judgment after death determines the eternal state of the soul. Not so, according to the Tradition and teaching of the Orthodox Faith. The particular judgment immediately after death only determines the state and “residence” of the soul in the spiritual world and that judgment is based on who our spiritual “friends” are. Do we have more converse with angels or demons? Do we devote ourselves more to the saints or to sinners? Are we attached to the world or to the Kingdom of God? Do we act like Satan or Christ? Whatever we are like, there we are placed in the spiritual world. And the demons are diligent in attempting to demonstrate that we are tied to them and not to Christ and so any and every unconfessed sin, no matter how seemingly small and insignificant is brought out by them as accusations against us and the angels on the other hand counter this accusation by a description of our righteous deeds which indicate our change of heart and life. But do not confuse this particular judgment and temporary disposition with the eternal disposition of the soul to be determined at the Great Judgment. Then, the soul being reunited with the body thanks to the general resurrection, each person will be judged by God Who sees within either the spark of grace or none and those who have that spark will be brought into the Kingdom of God and those who do not will be cast into outer darkness – finally and eternally. So you see that when we pray for the departed, we do so knowing that the final judgment has not yet occurred and while we don’t know what the exact needs of the departed are, we can simply lift them up to God calling out for His mercy.
Christ is Risen!