I believe EA's PC-based game is not online; however, if some one could correct me on that feel free to.
Meanwhile, Vivendi is working on two LOTR games of their own and one (developed by Turbine Entertainment) is online game (RPG, I believe) while the other is a real time strategy game.
Oh, and mouse, I did some research and your fears of EA making their own storylines is forbidden by their contract. Apparently, they can only create video game sequences at least mentioned in the movies.