4 We go on, “Your will be done as in heaven so in earth.” The Angels serve You in heaven, may we serve You in earth! The Angels do not offend You in heaven, may we not offend You in earth! As they do Your will, so may we do it also! And here what do we pray for, but that we may be good? For when we do God's will (for He without doubt does His own will), then is His will done in us. And we may understand in another and a right sense these words, “Your will be done as in heaven, so in earth.”
We receive the commandment of God, and it is well-pleasing to us, well-pleasing to our mind. “For we delight in the law of God after the inward man.” Then is His will done in heaven. For our spirit is compared to heaven, but to the earth our flesh. What then is “Your will be done as in heaven, so in earth”? That as Your command is well-pleasing to our mind, so may our flesh consent thereto; and so that strife be ended which is described by the Apostle, “for the flesh lusts against the Spirit, and the Spirit against the flesh.” When the Spirit lusts against the flesh, His will is even now done in heaven; when the flesh lusts not against the Spirit, His will is now done in earth.
There will be harmony complete when He will; be then the contest now, that there may be victory hereafter. Thus again, “Your will be done as in heaven, so in earth,” may be well understood, by making “heaven” to be the Church, because it is the throne of God; and “earth” the unbelievers, to whom it is said, “Earth you are, and unto earth shall you go.” When therefore we pray for our enemies, for the enemies of the Church, the enemies of the Christian name, we pray that His will may be done “as in heaven, so in earth,” that is, as in Your faithful ones, so in Your blasphemers also, that they all may become “heaven.”
Source: Sermons on Selected Lessons of the New Testament (New Advent)