Does someone else write the Lord of the Rings story?
No, J. R. R. Tolkien wrote all of The Hobbit and Lord
of the Rings stories entirely himself, nobody is writing any
However, his son Christopher Tolkien has taken many of his
father's earlier works and compiled and edited them into
publishable form. The first of these was The Silmarillion.
These stories however contain no hobbits and are mostly about the
Elves and wars that happened long ago in the First Age.