One of Tolkien's friend's makes this connection in the book "Tolkien: A Celebration", an excellent collection of essays by people who knew Tolkien and his work.
I have not read the work, but I would not be surprised. Several of Tolkien's biographers have made note of a strong augustinian philosophy in the work, which historically derives from platonism. I heard Joseph Pierce speak briefly on that subject a few months ago when he was touring with his book. Bradley Birzer also focuses heavily on it in his book, which came out a month or two ago.
Thanks. I just looked up Tolkien: A Celebration at Amazon.com. The book by Bradley Birzer looks interesting, as well, and was co-authored by Joseph Pearce.
The Platonist/Augustinian themes of the Lord of the Rings are obvious, as GOPcapitalist said. I'm just surprised more readers don't bring that up.