Try this...

Install Java first. You can download the latest version here: Java SE Downloads
Download the JRE offline installer & remove all other Java versions installed on your computer (via Add/Remove Programs) before installing this one.

Next, download the LW offline installer... after you choose your platform, a dialog box will pop up. Cancel that & use the option to download the offline installer
Lime Wire » Download LimeWire



See whether LW installs properly now.