It depends upon what interests you, but here are some more ideas to add on to
Rumil's list...
In one semester I start my student teaching for social studies and I always love how you can look at literature and see what it tells you about history (social, military, intellectual...etc). Many times Tolkien says he's not writing an allegory, which I will take his word for it, but you can learn a lot about history, by looking at the literature of the day. I think the same can be done with Lord of the Rings. For example, what technology is used in Lord of the Rings, what is it's purpose, and what does that tell you how technology was used during the time LOTR was being written? You can look at family structure, government...etc
Or certain intellectual topics like what is justice, in LOTR? What is wisdom?
Or maybe an analysis of a character. One time I wrote a paper on Grima and argued whether he was brainwashed by Saruman and was not in control of his actions or if he acted out of his own self-interests and should be held accountable.
The possibilities are endless and I would suggest to find whatever interests you, form an essential question from the topic, and make your argument.
