Try this...

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

Next, download the LW offline installer. When you click to download & a dialog box pops up, cancel it. Now use the option to download the offline installer
Lime Wire » Download LimeWire

Now try installing LW & see whether it works.