Lutherans have a pretty big discomfort when it comes to "doing theology" about what we call the Deus Absconditus--the Hidden God. That is doing theology about God has not made known, has not revealed, has not presented right before our eyes as it were. We instead "do theology" about the Revealed God, most specifically the God who meets us in and as Jesus Christ, His death and resurrection, and thus in the Sacraments.
Here what this would mean is that speculating on whether it is possible to "interact" with the departed is, basically, a non-thing. We would be heavily incredulous about it because we would have no reason, theologically, to accept it. For the same reason we don't place any emphasis on personal spiritual experiences at all really. All such experiences are subjective, and subjective things don't have any solidity to them in the realm of faith. Instead we look to the objective things, namely Scripture, the Gospel, the Sacraments, etc. For example we can't ever say where God isn't found, but we can say where God is found--God is found where He said He'd be found, in His Church through His Word and Sacraments. Further, if any personal experience were to come out and against God's Word and Sacraments we would consider such a thing to be, in a word, diabolical. Maybe not directly, but perhaps implicitly--it is certainly a position of faithlessness and is fundamentally not Christian (from a Lutheran POV); and many of us would point to the warning in Scripture wherein the devil is said as sometimes masquerading as an angel of light. Whether devilish or human the point would be the same: Real faith trusts in the objective word and promises of God, all else is fleeting, fanciful, and false.
Could God permit an "encounter" of some sort? Again, it's not out of question. There is the interesting story about King Saul and his encounter with the medium of Endor (the one that doesn't have an Ewok-filled moon). But this is a cautionary tale. It's simply not ours to speculate about what God might or might not do or let happen or not let happen; but to focus on what God has done and has said and has promised. We should, therefore, be very skeptical about claims of experiences of meeting the ghosts of the departed, or meetings with angels, or any number of assorted supernatural claims and experiences. For Lutherans the Christian life is not bound up in the "supernatural" and "spiritual", but is grounded in the solid, tangible realities of the Incarnate Jesus, His death, His resurrection, the preaching of the Word, the Scriptures, and the Sacraments.
-CryptoLutheran