The Lord of the Rings Volume 2: The Two Towers is a turn-based RPG released by Interplay in 1991. It runs only in DOS and so far as I have found is only available on floppy disk.
This game takes the player from the shores of the Anduin to the Dead Marshes. Gameplay switches between the three groups of: Aragorn, Gandalf, Legolas, and Gimli; Merry and Pippin; and Frodo and Sam. The game plays the same as Volume 1 and has all the same strengths and weaknesses. There are differences in the pictures for some characters, however. You can also carry your saved game from Volume 1 into Volume 2.
Since this game is more or less the same as Volume 1, if you enjoyed the first, you will enjoy the second.