As was said, Lightroom doesn't have the same need for a scratch disk that Photoshop does.
But, I'm definitely a proponent of having at least one "data drive" outside of your system drive. A lot of peope go a lot further than I have on my 5-yr-old work station, so I'll just use my setup as a "minimum": my 1/2 TB "data drive" has current shoots/images I'm working on (plus my music ligrary
) and then two important Lightroom resources: I have my LR catalog on it, which has both the metadata "stuff" and the Previews for all my catalog images. Then, I also keep the Camera Raw Cache, which holds 1:1 previews/Develop module previews for LR (as well as Photoshop Camera Raw if you have it installed).
By default, both these things are created in a directory that is likely on your system drive so you have to change them yourself. You change the Camera Raw cache location through Lightroom in the Edit/Preferences dialog and in the File Handling tab. There is also a size setting that is by default way to small for practical use -- I'd say a bare minimum of 5GB, but typically people set it quite a bit higher.
Your Catalog can be moved in different ways.
You also can designate a location for your catalog backups -- when the backup dialog pops up, you can click to choose a new location.