I would highly recommend Peter Kreeft's The Philosophy of Tolkien.
I've read parts of the Silmarillion (though familiar w/ the overall story) and am halfway through reading a collection of Tolkein's letters. It all depends on what you mean by a Catholic work. I also wouldn't explicitly say it's a Catholic work mostly because Christ is never mentioned! However... there is a strong sense of Catholic religious philosophy imbued in Middle Earth which is what Tolkein means by a "fundamentally religious and Catholic work" without using direct allegories on purpose (i.e. the route C.S. Lewis went in the Chronicles of Narnia).
Here are a couple suggestions for further reading on Catholicism's influence in LOTR:
1) A popular-level book done in Thomistic style by Peter Kreeft: https://www.amazon.com/Philosophy-Tolkien-Worldview-Behind-Rings/dp/1586170252
2) This one's on my shelf that I've been meaning to read, but it's a lot more academic in nature and concerns more modern Catholic inspirations he took in his writing: https://www.amazon.com/Tolkiens-Modern-Reading-Middle-earth-Beyond/dp/1943243727/ref=sr_1_1?crid=2FE8862L468IJ&keywords=word+on+fire+tolkien&qid=1651292563&s=books&sprefix=word+on+fire+tolkein%2Cstripbooks%2C101&sr=1-1
But there is a lot you can learn from the book and a lot of it relates directly to Catholicism.
Catholic Philosopher and writer Peter Kreeft even has a book talking about it: https://www.amazon.com/-/es/Peter-Kreeft/dp/1586170252
Peter Kreeft is the go-to on LOTR in my opinion.
Youtube:
Book:
Two of the best names to look into on this are Peter Kreeft and Joseph Pierce.
Kreeft wrote a book called The Philosophy of Tolkien: The Worldview Behind the Lord of the Rings, and Joseph Pierce has a number of books on the Lord of the Rings.
I would however state that I very much disagree with these authors when they say that The Lord of the Rings is a intrinsically Catholic Novel. The Lord of the Rings is first and foremost a fantasy novel, and I think it is counterproductive to look for Catholic truth and theology in it if that is what you are truly seeking. If you want to read something for the sake of your spiritual life pick up anything from Jacques Philippe if you want something contemporary, or start with St. John of the Cross if you want something a little more deep, from there you can have your choice of great moralists, saints and doctors to study.