Can atheists appreciate/understand Lord of the Ring?

[Aganzir]

Yes.

I wonder if English people understand them better than we who are not from England? Do I understand Narn i Chîn Húrin better because I'm Finnish and it's based on the Tale of Kullervo? Does a religious non-Christian understand the books better or worse than a non-religious person raised in a Christian country because they don't share Tolkien's cultural heritage?

Religion/spirituality is just one aspect among many that makes up a person. The fact that somebody doesn't believe in something doesn't mean they're not able to relate to people who do or that they don't understand what religion or belief are about. Many non-religious people I know are very well-versed in different religions; better so than many religious people I know. A non-Christian can know more about the Bible than a Christian - can even have read it more times.

Also, while Tolkien's Legendarium has many Christian elements, it's not an allegory. Therefore understanding shouldn't depend on your own religious background. The depth of the books is not just for understanding, it's for experiencing.

As you keep posting on the Downs, you'll come to find there are many agnostic, atheist and non-religious members (yours truly included). That's what the discussion forum is for - talking about how we understand the books. And as you read these discussions, it's up to you to decide if a non-religious Tolkien enthusiast can fully understand them, or understand them as you do.