St. Augustine of Hippo in his commentary on the Sermon on the Mount (II, 11) shows a correlation between the seven petitions of the Lord’s Prayer (Matt 6:9-13) and the Beatitudes (Matt 5:1-12).
First, concerning the petition “Our Father which art in heaven, Hallowed be thy name” he says: “If it is the fear of God by which are made ‘blessed the poor in spirit, for theirs is the kingdom of heaven,’ let us ask that the name of God be hallowed among men, a reverent fear abiding for ever and ever.”
Second, concerning the petition “Thy kingdom come” he says: “If it be piety by which ‘the meek are blessed,’ let us pray that His kingdom may come, that we may become meek, and not resist Him.”
Third, concerning the petition “Thy will be done in earth, as it is in heaven” he says: “If it be knowledge by which ‘they that mourn are blessed,’ let us pray that His will may be done as in heaven so in earth; for if the body consent with the spirit as does earth with heaven, we shall not mourn.”
Fourth, concerning the petition “Give us this day our daily bread” he says: “If fortitude be that by which ‘they that hunger are blessed,’ let us pray that our daily bread be this day given us, by which we may come to full saturity.”
Fifth, concerning the petition “forgive us our debts, as we forgive our debtors” he says: “If it is counsel by which ‘blessed are the merciful, for they shall obtain mercy,’ let us forgive debts, that our debts may be forgiven us.”
Sixth, concerning the petition “lead us not into temptation” he says: “If it be understanding by which they of ‘pure heart are blessed,’ let us pray that we be not led into temptation, lest we have a double heart in the pursuit of temporal and earthly things which are for our probation.”
Seventh, concerning the petition “deliver us from evil” he says: “If it be wisdom by which ‘blessed are the peacemakers, for they shall be called the sons of God,’ let us pray to be delivered from evil; for that very deliverance will make us free as sons of God.”
Quotations from St. Thomas Aquinas, Catena Aurea: Commentary on the Four Gospels Collected Out of the Works of the Fathers, Vol. I, Part I (Oxford: John Henry Parker, 1841).