That is an interesting citation, particularly considering that (so far as I understand), Lutherans do not consider Holy Orders in the same way that Catholics do (as a sacrament).
But it didn’t answer the specific questions: is there an accepted code of Canon Law within LCMS that provides standardization of the legal process (to include excommunication)? Also, is there some variety of an appeals process?
Although we do not normally term it as such, Lutherans can call ordination a sacrament, if that is properly understood. From the Apology of the Augsburg Confession, Article XIII, The Number and Use of the Sacraments:
"But if ordination be understood as applying to the ministry of the Word, we are not unwilling to call ordination a sacrament. For the ministry of the Word has God's command and glorious promises, Rom. 1, 16: The Gospel is the power of God unto salvation to every one that believeth. Likewise, Is. 55, 11: So shall My Word be that goeth forth out of My mouth; it shall not return unto Me void, but it shall accomplish that which I please. If ordination be understood in this way, neither will we refuse to call the imposition of hands a sacrament. For the Church has the command to appoint ministers, which should be most pleasing to us, because we know that God approves this ministry, and is present in the ministry. . . ."
But it didn’t answer the specific questions: is there an accepted code of Canon Law within LCMS that provides standardization of the legal process (to include excommunication)? Also, is there some variety of an appeals process?
It's not that legally detailed. The main issue is that of impenitence, persistent refusal to repent, after repeated admonition. What particular type of sin is involved is secondary; the problem is unrepentance.
Also, the pastor doesn't undertake and apply excommunication all on his own. He usually works first with the congregational lay elders, to try to lead the sinner to repentance. Then if the impenitent refuses to listen, the pastor and elders tell it to the church. If the impenitent refuses to listen to the church, and excommunication is then agreed upon by the congregation, it is carried out by the pastor, as the one entrusted with the public exercise of the Office of the Keys.
In practice, though, in recent decades, excommunication is rarely done.