J. R. R. Tolkien's lifelong interest in Philology, the study of change and development in language, is one of the foundations of his narrative. Research a study of comparative languages, particularly as it applies to a language family that interests you culturally.
Tolkien's Lord of the Rings has attracted the work of many illustrators. Tolkien himself was a gifted amateur illustrator and a number of his illustrations for his stories have been published. Study Tolkien's illustrations and discuss the ideas, artistic movements, and individual artists that you believe may have entered into his style.
Tolkien served in the trenches in World War I during the Somme offensive. Look at both his biography and at narratives of the battle of the Somme and attempt to find reflections of his experiences in Lord of the Rings.
For a time in 1965-66, Tolkien and his publishers were involved in a battle with Ace books over their unapproved paperback edition of Lord of the Rings. Investigate the history of copyright laws, and discuss the long running problems of British authors with American copyright laws.
Some critics have noticed the similarity between the society Tolkien drew in the Shire and the social ideas of William Morris. Study the ideas of Morris about work, art, and society, and discuss the extent to which the picture Tolkien draws of the Shire agrees or diverges from those ideas.