Go to Control Panel> Remove Software and remove all version of Java.
Uninstall LW as well.
Then re-install Java with the JRE offline installer, reboot and then install LW again.
If LW still doesn't recognize the Java version, uninstall LW again and as well the Java.
Put both installers on your desktop. Install LW and see whether it takes the installer exe of Java and installs it (that what it did with mine when I had once the problem). If not, it will most likely asked to download the Java. You can try this and see if it works.
If it doesn't, download an older JRE Java version (1.5.0-05 or _06) from here and install it with the offline installer.
http://java.sun.com/products/archive/ 