Which version of LW are you trying to install?

Which version of Java are you using? Do you only have one Java version installed on your computer?
If you've already updated your Java to the latest version, try this older version of Java 6 (if you're trying to install LW 5 then you'll need Java 6 & so the other older Java mentioned earlier in the thread will be no good): Archive: Download Java Platform Standard Edition (Java SE) 6u5
Install that Java, reboot & then see whether LW will install properly.

If you're trying to install LW 5 basic, you could try installing LW 4 basic & see whether you get the same error. You can download 4.18.8 from LW's older versions page: Lime Wire » Download Out-Of-Date Installers

If you have Pro, you can download 4.18.8 by clicking on the 'Get LW PRO Classic' link on the left of your personal download page.

Read this before installing an older version of LW: Just make sure that you have your current installer saved, because installing another version of LW will remove whatever you have installed at the moment. And if you have a Pro version which you can't update - you would lose that version!!

If you can install LW 4 without a problem, just try installing LW 5 & let it automatically uninstall LW 4... don't uninstall LW 4 first. See whether that makes any difference.