What Can the Tolkien Estate Do With Lord of the Rings?

This is the big one: Tolkien’s estate, alongside publisher HarperCollins, have the publishing rights to The Lord of the Rings and The Hobbit as Tolkien’s original novels. They control any reprints or re-releases of the original books, as well as the other connected novels and anthologies that were released posthumously from J.R.R. Tolkien’s notes—including The Silmarillion, and works like The Unfinished Tales of Númenor and Middle-earth.
The Tolkien Estate also retains the licensing rights to those latter works—it’s only the non-publishing rights for Lord of the Rings and The Hobbit that have gone elsewhere.