Long ago, when I was on my mission, my companion and I attended a funeral. The specific denomination has been lost to time, but it was a Protestant Christian church. At one point in the service, the congregation stood and recited the Lord’s Prayer. I joined in. My companion stood, but she didn’t say it, though I’m not certain if it was because she didn’t know it well enough to say it, or because she thought it was wrong. Her reaction to me saying it – “You know this?” combined with a look like I was going to Hell – led me to think it was sort of both. I merely shrugged and said, “Sure,” and that was all we ever said to each other about it.
Should a good Mormon recite the Lord’s Prayer when visiting another church? Sure, why not. When visiting other churches or other religions, I’m a when-in-Rome person. Unless there is something unethical or immoral (though I’ve never actually been in a such a situation when visiting), I prefer to join in with the rest of the congregation. I do try to be aware of when I should refrain from joining in because I am not a member of that faith, however, so as not to offend – such as partaking of their Communion. Still, when visiting a Presbyterian church at one time, the visitor pamphlet they had in with the hymnals said that visitors were encouraged to participate regardless of whether they were members of that church or even Christian, so I took their Communion.
In the specific case of the Lord’s Prayer, I would argue that reciting it is far from anything immoral. Sure, we have the “avoid vain repetitions” rule, with which I have no disagreement, but repetition does not necessarily mean vain. Also, since I don’t recite it regularly as part of church or personal worship, it is probably less repetitive than most of my prayers (for example, it is a rare prayer that doesn’t include things about my family and work, but such pleadings are not without sincerity) and leaves me with more to ponder.
Now, I’m certainly not advocating that the Lord’s Prayer be incorporated into LDS church services, but I find it to be a nice prayer when visiting other churches, and I’m happy to join their congregation in saying it.