First, if she hasn't already, read the appendices at the end of LOTR. Some of it can be skimmed, but there is some important info in there, which Peter Jackson is utilizing in the Hobbit Movies.

Then, the Silmarillion, in the order I suggested. Remember, this book was compiled and edited by Tolkien's son from his father's notes.

After that, either Unfinished Tales or Children of Hurin. I have not read the later and only partially read the former. Unfinished Tales contains some great stories and back story, but it sort of a scholarly book where Christopher Tolkien documents the various versions of the stories and how they evolved.

A reading of Tolkien's essay "On Fairy Stories" is highly recommended.

A biography of Tolkien is also helpful.

I think I suggested this before, but the website The One Ring is an excellent site for fans. Click through to their Library section for infinite information.

Another great site is The LOTR Project.Here you can find the resources you need while reading, including timelines, family trees, and maps. And not just maps, but interactive maps that show the routes characters take on their adventures. Very nice.