Now that's a whole other can of tuna. Tolkien was pretty clear on some occasions that he didn't want people to think Lord of the Rings was about anything other than Lord of the Rings - he did not like allegory. There are plenty of stories that abound with Christian symbolism, of course - I'm told Chronicles of Narnia lays it on pretty heavy, for one - but I don't remember LotR being one of them. It's been a while and I could be wrong.
And I guess now that I'm really thinking about it, Scrooge's first visit is a warning that he's hellbound if he doesn't change his ways. So fine - I suppose there are Christian symbols in the story. The Christian nature of the holiday just doesn't seem to be the focus.