The system for LOTR is called CODA and is rather like a cross between RuneQuest crossed with Traveller with Advantages and Disadvantages from the Hero System and Feats from Dungeons & Dragons 3e. This is not to decry the system, it is clean, functional and well described, although it has been criticised for poor system testing of the first edition.
The game is the second licensed game for the setting, the other being the Middle Earth Role Play from Iron Crown Enterprises.