That's because it is not the program but an alias. Double-click it & it will open LW. If you want to know where LW program is go to your menu bar & pselect 'Go' > Applications & you'll probably find the folder at the bottom of the applications folder. Or if you have the folder in list mode it will be under L for Limewire. What I like to do is to trash the alias, go to the program folder & drag & drop LW into the Dock. Then it's always there & easy to control. If you don't like the alias on your desktop you can use my technique & trash the alias.

When you install LW, the LW folder is installed in your Applications folder & an alias is put onto the desktop.