k one is a disk image compacted (the dmg), the other is the mounted disk image with the installer inside. Ignore both of those for now. On the menu bar, use the Go menu & choose Applications & find LimeWire folder. Open that folder, the LW program will be inside. Drag & drop it into the dock. Remove the other LW files from desktop. Make a back up of the dmg. Now when you wish to open LW you simply click on the LW icon in the dock.

BTW sorry for the very late reply.