Luther preceeded both John Calvin and Joseph Arminius. So he's not borrowing from either one of them when he wrote his position on how a person is justified. Here is the Lutheran position on both Free Will and Justification.
Article XVIII: Of Free Will.
1] Of Free Will they teach that man's will has some liberty to choose civil righteousness, and to work 2] things subject to reason. But it has no power, without the Holy Ghost, to work the righteousness of God, that is, spiritual righteousness; since the natural man 3] receiveth not the things of the Spirit of God, 1 Cor. 2, 14; but this righteousness is wrought in the heart when the Holy Ghost is received 4] through the Word. These things are said in as many words by Augustine in his Hypognosticon, Book III: We grant that all men have a free will, free, inasmuch as it has the judgment of reason; not that it is thereby capable, without God, either to begin, or, at least, to complete aught in things pertaining to God, but only in works of this life, whether good 5] or evil. "Good" I call those works which spring from the good in nature, such as, willing to labor in the field, to eat and drink, to have a friend, to clothe oneself, to build a house, to marry a wife, to raise cattle, to learn divers useful arts, or whatsoever good 6]pertains to this life. For all of these things are not without dependence on the providence of God; yea, of Him and through Him they are and have their being. "Evil" 7] I call such works as willing to worship an idol, to commit murder, etc. 8] They condemn the Pelagians and others, who teach that without the Holy Ghost, by the power of nature alone, we are able to love God above all things; also to do the commandments of God as touching "the substance of the act." For, although nature is able in a manner to do the outward work, 9] (for it is able to keep the hands from theft and murder,) yet it cannot produce the inward motions, such as the fear of God, trust in God, chastity, patience, etc.
Article IV: Of Justification.
1] Also they teach that men cannot be justified before God by their own strength, merits, or works, but are freely justified for 2] Christ's sake, through faith, when they believe that they are received into favor, and that their sins are forgiven for Christ's sake, who, by His death, has made satisfaction for our sins. 3] This faith God imputes for righteousness in His sight. Rom. 3 and 4.
Excerpts from the Book of Concord: The Lutheran Confessions as found at:
http://www.bookofconcord.com/augsburgconfession.php#article18