What do Lutherans teach regarding Second Death (the ultimate fate of the Unjust as described by the book Revelations)? Are Lutherans Annihilationists? Do they believe in a traditional hell of eternal torture? Or something else?
Traditional Lutherans view that the wages of sin is death. That is to say the punishment of sin is separation from God. In other words, God punishes sin with sin. He allows the consequences of sin to run its course in death and destruction. That is called the alien work of God.
For those with saving faith in the blood of the Lamb, the redeemed soul will be given a new glorified body at the end of the age.
In Lutheran theology the unregenerated soul comes back in a corrupted body for the general resurrection. At that time there will be a gnashing of teeth, directed at God and perhaps also at the general condition of living in a cursed world apart from God.
The second death is described in a poetical way in the book of Revelation as the destruction of the unregenerate in the lake of fire. In that sense, technically it is not annihilation. Rather, it is kind of like being sucked into a cosmic spiritual black hole. That black hole/time freeze/oblivion concept appears to be what Revelation 20:10 is depicting, with the word "βασανισθήσονται" (torture, agitation) being the "flotsam & jetsam" agitation that takes place in the lake of fire.
While the black hole concept has its advocates, the most popular theological construct of hell for Lutherans is that which is depicted in C.S. Lewis' novel "The Great Divorce."
Having said the above, an annihilation view was very popular among conservative European Lutherans in the 19th century. Evidently, they considered a view of an eternal torment in hell as an Aberglaube, superstition. For example, R.C.H. Lenski in his commentary on Revelation 20:10 (writing against interest) quotes the conservative scholar Theodore Zahn who writes:
What purpose could God have in such eternal torment? As for men, a corpse has no more sensation. Man is not immortal, nor is the devil. The blessed are made immortal by God. Fire burns till the objects thrown into it are consumed. It may take a long time to do the consuming, but this process does not continue for ever. To be thrown into the lake of fire and brimstone means to be consigned to annihilation. This term 'lake' is taken from the Dead Sea, and 'lake of fire and brimstone' from the annihilation of Sodom of Gomorrah.
The controversial nature of the question is how to best interpret the Augsburg Confession, in which it states:
They condemn the Anabaptists, who think that there will be an end (finem) to the punishments of the condemned men and devils. (Trigl. 51, XVII, 4)
A helpful way to understand the Augsburg Confession on this matter is to note its embedded historical context as being a rejection of Origen's universalism teaching. For example, in Confessing One Faith: A Joint Commentary on the Augsburg Confession by Lutheran and Catholic Theologians, a reference is made to this section of the Augsburg Confession (emphasis added):
The Anabaptists had incorporated a teaching, that was long rejected, of the restoration of all things at the end of time (apokatastasi in connection with Acts 3:21 and groups of Jewish origin, which awaited an earthly 'thousand year' rule in this world preceding the resurrection of the dead.
There was a reason for including this article in the CA as a precaution: the reformers wanted to protect themselves from being taken for one of the enthusiastic and apocalyptic sectarian groups. (p. 82)
In one of the preliminary drafts of the CA (NA 16, cf. BSLK 72) the name of Origen was mentioned: 'the followers of Origin.' So-called 'Origenism' was often rejected in the early church... (p. 92)