And you know, I think the groups near me use the Lord's Prayer partly b/c it's something that everyone knows, regardless of religious affiliation or lack thereof. I have never been a part of any organized religion, either as a child or an adult, but I knew enough of the prayer to follow along when I started Alanon.
I don't think the use of it is a conscious effort to force Christianity on anyone, I just think it's a simple common denominator-type thing, an easy and fairly comfortable way to close the meeting.