Wow. I'm not too sure.

When I download LimeWire, I get a file on my desktop named: LimeWire Installer. When I double-click it, it begins the installation process. I would say that something is messed up if your system picks the QuickTime application to run the installer (Obviously).

I would go to the Apple Discussion Boards and ask there. They will probably be able to tell you how to fix this. Here's the link.
Assuming, of course, that you are using OS 9.x. If not, navigate through the site to find the Discussion Board for the system you are using. There are alot of very helpful people there.

Good luck.