You've downloaded and installed LW already, so there is no need for entering any password or login.
Besides, when you've bought LW pro from the official site you have received a email with the personal download page for you. Use the login and password for this, if you wish to redownload the LW installer.exe.
I assume you paid $18.88 for it and purchased it from this website:
http://www.limewire.com/ 