I have never done a systematic study of the Lord's Prayer, but I was struck by some comments made by Dr. Pius Parsch in his classic study The Liturgy of the Mass. He described the logical relationship between the seven petitions of the Our Father in a way that made me realize for the first time that the petitions are not a random series, but in fact are related to each other. Also, although he doesn't emphasize this, a Eucharistic interpretation is quite possible.
What he points out is that of the seven petitions the first three reflect, in reverse temporal order, the purpose of the life of man and the last three represent, in reverse temporal order, those things that are detrimental to the fulfillment of a truly human life. The logic of the first three petitions goes from 1) doing God's will, which 2) accomplishes the coming of His kingdom, which then 3) gives glory, honor (hallows) His name. The three barriers to achieving this are 1) our sins (trespasses, debts), 2) temptations, and 3) the Evil One (which is how πονηροῦ is often translated). This moves from the Evil One to temptation to sin! Note that the first word in the prayer is "Father." The "our" comes after "father" in the Greek. The last word is "The Evil One." Also note, as Parsch did, the two "as" statements in the third and fifth petitions, enhance the sense of a diptych around the central, fourth, petition.
The middle petition, for daily bread, is clearly highlighted by this structure. It reflects our desire to have what we need now on earth to fulfill our humanity. Logically, this is grace, but in fact it is a prayer for bread. Parsch doesn't put a particularly Eucharistic spin on this petition, but that has been done in the tradition, especially those, such as St. Jerome, who have translated the petition as "Give us this day our supersubstantial bread." (See this article by Fr. Benjamin Reese for a linguistic justification of this translation; as it turns out the word appears nowhere else in Greek.) What is it that helps us 1) to fulfill our humanity, the first three petitions, and 2) to avoid those things which are barriers to that fulfillment, the last three petitions? The Eucharistic Bread of Life!
For the early Christians bread already had a significance beyond physical sustenance. First of all, it had a social significance in the ancient Mediterranean cultures. Witness, for instance, the word "companion," which helps us remember that sharing bread is a component of partaking of bread. "As this broken bread was scattered upon the mountains, but was brought together and became one, so let thy Church be gathered together from the ends of the earth into thy kingdom, for thine is the glory and the power through Jesus Christ for ever." (Didache 9:4). Further, of course, bread has a spiritual, Eucharistic significance.
The prayer clearly lays out the fundamental spiritual dynamic of human existence. We are stuck in the spiral of sin. The only way to get beyond that spiral to the movement of grace towards God is through the Word Incarnate become the Bread of Life. There is a movement down and a movement up. It is no mistake that the Lord's Prayer appears where it does in the Liturgy, right after the consecration and at the head of the Communion Rite.
This is not a fanciful, "spiritual" interpretation imposed upon the text from later reflection. It reflects the logic of the text itself. This prayer was clearly composed very carefully, which does not itself call into question its dominical origin . If John of the Cross can so carefully compose spiritual poetry in a dark prison, our Lord could certainly have composed this prayer while spending those hours at night in prayer. It would be a spiritual masterpiece, even if it weren't dominical.
I don't always agree with Parsch's interpretation of the liturgy. He falls victim to the archaistic dismissal of medieval developments that Cardinal Ratzinger criticized in The Spirit of the Liturgy. On the other hand, this book can be very insightful and spiritually upbuilding.