Best advice is to remove all your Java versions. Then go to Start menu -> Programs -> LW -> Uninstall.
2. Delete your LW preferences folder as described in link in post #2 above point 3 in that link page.
3. Run this utility:
Crap Cleaner
4. Download and install the "OFFLINE" Java version
5. Download and install the "OFFLINE" LW version (the non-preferred option).
My guess is one of the Java versions is not working properly for you. Question is which one. Try Java 1.6 first. If not work correctly, then remove it, and download and install java 1.5 instead.