Warning: this book will cause you to read (or re-read) other books.
Ever since I finished this book, I have been itching to read C.S. Lewis's "space trilogy", as well as get my copy of "The Hobbit" back from my friend, so I can start reading it to my children.
"Lord of the Elves and Eldils" does an excellent job of providing background information about C.S. Lewis and J.R.R. Tolkien: their lives, their friendship, their academic specialties, their faith, and personal philosophies. It also provides added insight into things that you may have glossed over or just plain misunderstood when you first read the fiction of Tolkien or Lewis.
Although the book is about the fictional works these men, the true insights of the book come from an examination and analysis of their non-fiction. For example, passages in "Miracles" and "Mere Christianity" help to better understand "Perelandra" and "The Last Battle".
The only unfortunate thing is that Tolkien did not leave behind as large a legacy of non-fiction as Lewis did, so we don't have as much directly from Tolkien and instead must be satisfied with what his son, Christopher, and others have said about him. (This is not meant as a negative against this book, but rather to explain the challenges faced in his analysis of Tolkien and why there is more about Lewis.)
The footnotes show the depth of the research that went into writing this - not only research about Tolkien and Lewis, but also about their critics and detractors. You may think you are reading something about your favorite authors, but what you end up getting is an education in literary criticism through an example of how it is done well.
This is an excellent book, but as I said before, do not start reading this unless you have time in your reading schedule for at least 3-6 more books when you are done.