To open the LW program you simply double click it with your mouse cursor, else, click it once from the Dock. What you are doing is Control clicking the program & choosing open which is opening the contents of the program package. Don't get confused with windows. The equivalent key to Control on mac is the Apple/Command key. It has an apple icon & ⌘ icon on it.

Use the Go menu & select Applications. Then find the LimeWire folder & open it. Then drag & drop the LW program into your dock. Now when you wish to open the program you simply click it once from your Dock.

Normally to open an OSX program you simply double-click it.

(BTW Mac OSX programs have most of their support files within the program package so when you wish to uninstall, you normally only need to drag & drop the program into the trash & it's all gone. No need for an uninstaller. )