When I had my Gamecube I had two LOTR based games for it,
The Hobbit, and
The Third Age. Both are quite fun, I might recommend The Hobbit over the other, It was more action based and less like a Final Fantasy game (Third Age had combat like FF10/X-2) And it's also on the PC. Small thing is I remember beating The Hobbit in about 2 days, while Third Age took me quite a while, however the story of Third Age... Eah, not the best.