What does Lutheranism teaches in regard the eastern orthodox doctrine of theosis?

It is inaccurate firstly, to say that "[t]his practice/doctrine seem to come from the so called 'desert fathers' and/or 'cappadocian fathers".

Rather, the amount of quotes from the writings of church fathers shows that the focus of the incarnation of Christ is directly related the believers' deification.

Justin Martyr, a second-century apologist, is one of the earliest witnesses to explicitly teach that man may become God in God's salvation.

Let the interpretation of the Psalm be held just as you wish, yet thereby it is demonstrated that all men are deemed worthy of becoming “gods,” and of having power to become sons of the highest.... (Dialogue with Trypho)

Shortly after, Irenaeus of Lyon:

For we cast blame upon Him, because we have not been made gods from the beginning, but at first merely men, then at length gods; although God has adopted this course out of His pure benevolence, that no one may impute to Him insidiousness or grudgingness. He declares, “I have said, Ye are gods; and ye are sons of the Highest.” (Against Heresies, Bk. IV, ch. 38, sec. 4)

Clement of Alexandria uses Psalm 82:6 to show that our sonship in Christ is synonymous with our becoming God:

Accordingly this grace is indicated by the prophet, when he says, “I said that ye are gods, and all sons of the Highest.” For us, yea us, He has adopted and wishes to be called the Father of us alone, not of the unbelieving. (Protreptikos 12)

Being baptized, we are illuminated; illuminated, we become sons; being made sons, we are made perfect; being made perfect, we are made immortal. “I,” says He, “have said that ye are gods, and all sons of the Highest.” (Paedagogus, Bk. I, ch. 6)

I think these are sufficient and you can get more from Athanasius, Gregory of Nyssa, Palamas, John of Damascus and so on.

Regarding the question, there are traces of deification found in Luther passages that seem to support the Finnish claim (Mannermaa and his counterparts) on deification at the center of Luther's theology.

In the Christmas sermon of 1514:

Just as the Word became flesh so is it necessary that the flesh become the Word. For the Word becomes flesh precisely so that the flesh can become Word. In other words, God became man so that man may become God. Thus power becomes powerless so that weakness may become powerful. The Logos put on our form and manner, image and likeness, so that he might clothe us with his image, form and likeness. Therefore, wisdom became foolish, so that foolishness might become wisdom. And so with regard to all other things that are in God and us, in everything he assumes ours, so that he might confer onto us his …

The second from a 1525 sermon:

And so we are filled with “all the fullness of God.” This phrase, which follows a Hebrew way of speaking, means that we are filled in all the ways in which God fills; we are filled with God, and he pours into us all his gifts and grace and fills us with his Spirit, who make us courageous. He enlightens us with his light, his life lives in us, his beatitude makes us blessed, and his love causes love to arise in us. Put briefly, he fills us in order that everything that he is and everything he can do might be in us in all its fullness, and work powerfully, so that we might be divinized throughout -

In Christ Present in Faith: Luther's View of Justification, Tuomo Mannermaa speaks of this reality:

Because faith means a real union with Christ, and because in Christ the Logos is of the same essence as God the Father, therefore the believer’s participation in the essence of God is also real....

In other words, justification by faith is not merely forensic but involving a union of the divine life. It is not something that we are convinced of in our mind; it is something that we receive when we are joined to the Lord as one spirit (1 Cor. 6:17). When the living Christ indwells us, His faith becomes our faith. We believe because He is faithful, and He cannot deny Himself in us (2 Tim. 2:13). In our organic union with Him, His faith becomes our faith, and our faith is His faith.

The "happy exchange" according to Luther involves Christ's assumption of our sin and our assumption of His righteousness. In his Commentary on the Epistle to the Galatians, Luther speaks of this exchange in relation to faith and to our union with Christ. He says:

Faith connects you so intimately with Christ, that He and you become as it were one person. As such you may boldly say: “I am now one with Christ. Therefore Christ’s righteousness, victory, and life are mine.” On the other hand, Christ may say: “I am that big sinner. His sins and his death are mine, because he is joined to me, and I to him.