Do you need the disc to play lord of the ring online?

Nope.

Lord of the Rings Online (LOTRO) occasionally has disk sets, which include the packaged game on disk(s). This also usually includes other in-game items.

However, the game itself is available for free download from the official website. While you do have to buy some areas to access them, those are also available online through the official website, so it is not necessary to buy the game on a disc, unless you want to.