These are the two traditions that cover what you want to know.
2. For our group purpose there is but one ultimate authority — a loving God as He may express Himself in our group conscience. Our leaders are but trusted servants; they do not govern.
This means that decisions regarding the group are made by the members of that group,who have(hopefully)considered all the implications of any decision very carefully.
4. Each group should be autonomous except in matters affecting other groups or A.A. as a whole.
And this means that the group is free to conduct itself as it's members see fit,and to make decisions regarding format and group business,so long as those decisions do not have an impact on other groups or AA as a whole.
If your group chooses not to use the Lord's Prayer it would be wise to accept that decision and to abide by it when you chair.If it troubles you too greatly,maybe you should consider exploring other meetings.
I do understand your loyalty to the group,and your feelings about the prayer.But the traditions were developed over 60 years ago,after much debate and strife over how groups should operate.They protect the group and the individual as well.
Regards,
phoenix