Hate to say this, but just because it's non-profit doesn't mean it's exempt from Cease-and-Desist orders. For example, a fanfilm entitled The Hero of Time(obviously based on The Legend of Zelda) was going to be distributed freely and the creators were not going to make any money from it at all. However, Nintendo sent them a C&D, though allowed a short distribution of the movie.
Granted, not many were sad about this because said fanfilm was a terrible, terrible, miserable piece of crap, but still. If a company sees something and decides to issue a cease-and-desist, there really isn't much that can be done.
However, they could try fighting this on grounds that they aren't infringing on Warner Brothers rights since they do not OWN Tolkien's works. Warner Bros is merely allowed to use them.