Here is the Lutheran Study Bible, by the way: http://www.cph.org/t-tlsb.aspx
Luther on John, pp. 1774 and 1775
From the very beginning the evangelist teaches and documents most convincingly the sublime article of our holy Christian faith according to which we believe and confess the one true, almighty, and eternal God. But he states expressly that three distinct Persons dwell in that same single divine essence, namely, God the Father, God the Son, and God the Holy Spirit. The Father begets the Son from eternity, the Holy Spirit proceeds from the Father and the Son, etc. Therefore there are three distinct Persons, equal in glory and majesty; yet there is only one divine essence....The first man to attack the doctrine of the divinity of Christ was the heretic Cerinthus, a contemporary of the apostles. He presumed to fathom and comprehend this article with his reason. Therefore he declared that the Word was not God. And in order to support this view he cited the verse from Deuteronomy (6;4): "The Lord our God is one God"; and also (Deut.5:7): "You shall have no other gods before Me." With this sham he worked great harm. he gained a powerful following. Many Jews attached themselves to him, even some of those who had believed in Christ. It must be viewed as a manifestation of divine grace that Cerinthus assailed this article during the lifetime of the apostles; for this is what prompted John, the foremost of the apostles still living at the time, to write his Gospel. In it he proves this article conclusively: that Christ, our Lord and Savior, is true, natural, and eternal God with the Father and the Holy Spirit. John had a very good reason for basing his proof on Moses, since it was he of whom Cerinthus and his followers had boasted. Wresting Moses from their hands, mouth, and heart, John now quotes Moses in an attack against their blasphemous heresies and refutes them completely. This was a veritable masterstroke.
Therefore the evangelist John is a master above all the other evangelists, for he treats of this doctrine of Christ's divinity and His humanity persistently and diligently. he joins these two natures together. When Christ becomes man, He speaks to us, performs miracles, and dies according to His humanity. And then His divinity is also established with plain words.
Early Christian testimony affirms that the apostle John wrote the Fourth gospel. Yet the Gospel itself never states this directly. Instead, the author describes himself as "the disciple whom Jesus loved" and seems to mention other witnesses to the events of the Gospel. Critics have used these facts to suggest a number of other potential authors, but none of the suggestions are compelling. The references to the beloved disciple fit well with what we know of John in the other Gospels: that he was a member of Jesus' inner circle and a close comrade of Simon Peter in Acts; the other member of that inner circle--John's brother James--was martyred early on; Ac 12:2. The reference to other witnesses ("we") also shows up repeatedly in the Letters of John. Therefore, early Christian testimony appears sound and consistent in affirming John as the writer.