Whenever I lead the congregation in the Morning Prayer, I always make sure I have the Lord's Prayer written down and that I have it with me. I fear that the same thing would happen to me in the anxiety of praying in front of a large group of people.
The thing is - the Lord's Prayer is a corporate prayer. Think about the words - they include many repetitions of the words we and us. We are meant to pray it together.
Maybe that says something about how we are to live it out - corporately. Just as we can have problems praying it alone, I'm certain we will have problems trying to live it out alone. We need each other to live the lives that God intends.
Just one more reason to be part of the Body of Christ.