It Might be a Java issue.

First of all, install Java. Download the JRE offline installer & remove any other Java versions installed (via Add/Remove Programs) before you install the latest Java.
Java SE Downloads

After Java's installed, install LW. When you click to download the LW installer, cancel the dialog box which pops up...now use the option to download the offline installer.
Lime Wire » Download LimeWire

If this doesn't work you might try an older version of Java. 5.11.
Make sure you delete ALL Versions of Java before either Java Installation and use the offline installer.

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