Your LW downloads are saved to your computer. Since you don't even say what OS you're using, here's a reply for Windows

In LW tools > options > saving shows you the location of your saved folder. By default this is C:\Documents and Settings\your username\Shared.
So if you want to move your saved files from one computer to the other, just save & back up the files in this folder.
Then, once you've downloaded LW again, copy the files to your saved folder.