Do you have to begin every prayer with the exact words of the Lord's Prayer?
No. The passage is given as a pattern for prayer, not a required formula. It does not mean every prayer must open with those exact words. It indicates that when approaching God's throne, believers still give Him His due, recognizing Him as the Almighty and Heavenly Father.
Les teaches that Matthew 6 is commonly called the Lord's Prayer, but he prefers the disciples' prayer because the Lord gives it as an example for the disciples to use. The real Lord's Prayer, he says, is John 17. Here Jesus instructs the disciples how to pray. Verse 9 is a pattern, and it does not mean you have to open every prayer with these exact words. It does indicate that as we approach the throne room, even in this age of grace, we still give God His due, recognizing Him as the Almighty and as our Heavenly Father. Les notes this was still under the Law, to the Jew under temple worship, but the format carries over into us under grace.
After this manner therefore pray ye: Our Father which art in heaven, Hallowed be thy name.