I started Hans Dieter Betz's commentary on The Sermon on the Mount, which also comments on the Sermon on the Plain.
The Sermon on the Mount (Matthew 5:3-7:27) and the Sermon on the Plain (Luke 6:20-49) are similar, yet different. Both have beatitudes, the theme of non-retaliation, and other similar sayings. But the Sermon on the Mount is long and elaborate, and it emphasizes such things as the abiding value of the Torah and being perfect and righteous. The Sermon on the Plain, however, is more succinct and talks about the poor and mercy. Betz refers to the harmonizing view (held by Augustine and others) that both are two different sermons, delivered on two separate occasions. But Betz does not buy that, for both are parallel in the sense that they come soon after a story in which Jesus calls disciples, and they come soon before a story in which Jesus heals a centurion's servant. For Betz, both sermons descend from a common source, and the Sermon on the Mount was for Jewish-Christians (in that it stressed the Torah and generosity), whereas the Sermon on the Plain was for Greek Christians. Both try to flesh out what Christian discipleship entails. Betz dates the adaptation of the sermon to both groups to the time of Paul.
And yet, Betz appears to have some desire to harmonize the Sermon on the Mount with Paul, who denied that we can earn salvation through obedience to the law and stressed the role of the Holy Spirit in enabling us to live righteous lives. Betz says that the good deeds that the Sermon on the Mount promotes are not an attempt to earn salvation but rather are "'fruits' of insights into God's ways, and as such they 'deserve' salvation", and that "Paul would call them 'fruit of the Spirit' (Gal 5:22), rather than 'works of the law'" (page 97). At the same time, on page 46, Betz refers to how Augustine wrestled with the apparent absence of the Holy Spirit in the Sermon on the Mount, which is puzzling because the Christian would need the Holy Spirit's power to keep the Sermon's commands.
Evangelicals have sought to interpret the Sermon on the Mount in light of their view on the Gospel: that people need to accept Christ's sacrifice on the cross for their sins and be regenerated in order to live a truly righteous life. Many do so by saying that the beatitudes are about the need to be humble when recognizing one's sin, which leads a person to despair of any attempt to save himself, and thus to turn to Christ. Others maintain that, when Christ in Matthew 7:16-20 says that a good tree bears fruit, he is supporting the concept of regeneration----that people need to be born again (become good trees) and plant themselves in Christ in order to obey the commands of the Sermon on the Mount. I wouldn't say that there's absolutely nothing to that spiel. I just don't think that it's overly explicit in the Sermon on the Mount. To what extent is the spiel a legitimate reading of the Sermon on the Mount, and to what extent is it reading evangelicalism into the Sermon on the Mount, when the Sermon is saying something different?