Here's a brief commentary from Lutheran pastor Jordan Cooper who addresses the subject and provides some important nuance and context:
Augustine is not interested in talking about the relationship of God's sovereignty and human will, as becomes a focus among some Reformed thinkers much later; Augustine is chiefly interested in addressing the Pelagian heresy and thus places the focus on God's grace; so that for Augustine predestination is not about God making a sovereign decree to save some and not others (whether in the
Infralapsarian or Supralapsarian sense). Given the backdrop of the Pelagian controversy Augustine's interest is on the total and unequivocal essential importance of God's grace. Man's will is insufficient to bring him to salvation not because of God's sovereign decree, but because of human weakness through the Fall aka Original Sin, and thus it is impossible for a person to come to God or to be righteous before God through a pure and free human act of obedience (such as Pelagius taught). Thus for Augustine salvation only happens because God, out of His love and grace gives the gift of faith and salvation, and therefore apart from the grace of God, and the saving passion, death, and resurrection of Jesus it is impossible for a person to be saved.
Both Luther and Calvin leaned hard into Augustine, but they both came to radically different views on the subject of predestination and election. And, of course, Roman Catholicism is also tremendously Augustinian, but has a radically different view than either Luther or Calvin.
This means that it is possible for Roman Catholics, Lutherans, and Calvinists to all find material in Augustine's works. And the work of interpreting Augustine can become just as complex as any complex treatment of biblical exegesis.
As a Lutheran I don't have a problem admitting my Lutheran bias, and that, therefore I do read Augustine as a Lutheran. But from an objective stand point it would be wrong to claim Augustine was himself Lutheran--just as it would be wrong to claim Augustine was a Calvinist or even Roman Catholic (in the context of late medieval/early modern Reformation/Counter-Reformation debates). Augustine's work, and his arguments, involve a particular context. To a certain degree claiming Augustine exclusively by any party involves anachronism.
Augustine said things that Lutherans use to support our view.
Augustine said things that Calvinists use to support their view.
Augustine said things that Roman Catholics use to support their view.
But Augustine is before the visions of these three that occurred in the 16th century, he is writing in the context of Late Antiquity, not the Late Middle Ages/Early Modern Period. Augustine is not writing in the context of the particular historical and ecclesiastical issues of the 16th century, but of the late 4th and early 5th centuries. Augustine's chief ideological/theological nemeses are the Arian and Pelagian heresies, and also the Manichean religion which he was a member of for a time.
Augustine is known as the Doctor of Grace because God's grace is the the through-line of nearly everything he wrote. We see it from his commentaries and theological treatises, and even in his personal biography, the Confessions, where he recognizes in himself the deep darkness of sin and his own need for the Savior who graciously meets him, a sinner, in grace.
-CryptoLutheran