If we actually look at the biblical text of the Lord's Prayer, their today's gospel from Luke or its counterpart in Matthew the most striking feature is absence of the final doxology, "For thine is the kingdom..." None of the manuscripts of Luke or the oldest and best of Matthew contain it. Few scholar would try to argue that it is part of the biblical text.
As best we can find, the doxology first appears with the Our Father, in a document known as the didache, late first early second century. There is reads simply "For you have the power and glory forever."
It appears that over time this doxology, being sung after the Lord's prayer, was first copied into biblical manuscripts as a kind of side note, and later migrated in the text itself. This was the great problem of manuscripts. Much depended on the person copying the text, and the person copying the copy, and so on.
This is part of the great challenge for scripture scholars, to take the various manuscripts of each book, and try and discover the most likely original text. In 1979, Pope John Paul II, promulgated the New Vulgate, a new Latin edition of the Bible, based on, St. Jerome's Vulgate, but taking into account our best understanding of the original Greek and Hebrew texts.
It would make life simple if we could say, "Here we have the original text of each book of the bible written by a single author whose name we known for certain." That, alas, is not Christianity. We believe the Bible to be the inspired word of God, and we struggle each to understand it more deeply and live it. We do this in faith, trusting that the Holy Spirit not only guided the original human authors, but continues to guide the church in her understanding and right interpretation of The Books (Τά Βιβλία).