In his commentary on Hebrews 8, Owen explains that he agrees with the Lutheran interpretation of the old and new covenants:
The Lutherans, on the other side, insist on two arguments to prove that there is not a twofold administration of the same covenant, but that there are substantially distinct covenants and that this is intended in this discourse of the apostle.
Their arguments are
1. Because in the Scripture they are often so called (separate covenants), and compared with one another, and sometimes opposed to one another; the first and the last, the new and the old.
2. Because the covenant of grace in Christ is eternal, immutable, always the same, subject to no alteration, no change or abrogation; neither can these things be said of it with respect to any administration of it as they are of the old covenant.
…Having noted these things, we may consider that the Scripture does plainly and expressly make mention of two testaments, or covenants, and distinguish between them in such a way as can hardly be accommodated by a twofold administration of the same covenant…Wherefore we must grant two distinct covenants, rather than merely a twofold administration of the same covenant, to be intended. We must do so, provided always that the way of reconciliation and salvation was the same under both.
Here is an example of Luther on the old and new covenants:
From the above it will at once be seen what is the right and what is the wrong use of the mass, and what is the worthy and what the unworthy preparation for it. If the mass is a promise, as has been said, then access to it is to be gained, not with any works, or powers, or merits of one’s own, but by faith alone. For where there is the Word of the promising God, there must necessarily be the faith of the accepting man. It is plain therefore, that the beginning of our salvation is a faith which clings to the Word of the promising God, who, without any effort on our part, in free and unmerited mercy takes the initiative and offers us the word of his promise. “He sent forth his word, and thus [sic] healed them,”86 not: “He accepted our work, and thus healed us.” First of all there is God’s Word. After it follows faith; after faith, love; then love does every good work, for it does no wrong, indeed, it is the fulfilling of the law [Rom. 13:10]. In no other way can man come to God or deal with him than through faith. That is to say, that the author of salvation is not man, by any works of his own, but God, through his promise; and that all things depend on, and are upheld and preserved by, the word of his power [Heb. 1:3], through which he brought us forth, to be a kind of first fruits of his creatures [Jas. 1:18].
Thus, in order to raise up Adam after the fall, God gave him this promise when he said to the serpent: “I will put enmity between you and the woman, and between your seed and her seed; he shall bruise your head, and you shall bruise his heel” [Gen. 3:15]. In this word of promise Adam, together with his descendants, was carried as it were in God’s bosom, and by faith in it he was preserved, waiting patiently for the woman who should bruise the serpent’s head, as God had promised. And in that faith and expectation he died, not knowing when or who she would be, yet never doubting that she would come. For such a promise, being the truth of God, preserves even in hell those who believe it and wait for it. After this came another promise, made to Noah—to last until the time of Abraham—when a bow was set in the clouds as a sign of the covenant [Gen. 9:12–17], by faith in which Noah and his descendants found God gracious. After that, he promised Abraham that all the nations should be blessed in his seed [Gen. 22:18]. And this is Abraham’s bosom [Luke 16:22], into which his descendants have been received. Then to Moses and the children of Israel [Deut. 18:18], especially to David [II Sam. 7:12–16], he gave the plainest premise of Christ. and thereby at last made clear what the promise to the men of old really was.
And so it finally came to the most perfect promise of all, that of the new testament, in which, with plain words, life and salvation are freely promised, and actually granted to those who believe the promise. And he distinguishes this testament from the old one by a particular mark when he calls it the “new testament” [Luke 22:20; I Cor. 11:25]. For the old testament given through Moses was not a promise of forgiveness of sins or of eternal things, but of temporal things, namely, of the land of Canaan, by which no man was renewed in spirit to lay hold on the heavenly inheritance. Wherefore also it was necessary that, as a figure of Christ, a dumb beast should be slain, in whose blood the same testament might be confirmed, as the blood corresponded to the testament and the sacrifice corresponded to the promise. But here Christ says “the new testament in my blood” [Luke 22:20; I Cor. 11:25], not somebody else’s, but his own, by which grace is promised through the Spirit for the forgiveness of sins, that we may obtain the inheritance.
There is a decent chance Luther got that idea from Augustine, or maybe from just reading his Bible 🙂