Quite a few people had this problem with Java 6 update 1...you're the first one I've seen who has the problem with update 2
Like I said, I have update 2 & LW works fine (but it did for me with update 1 as well, it's only some people that seem to have trouble).

Keep the link to the Java version that works for you, or use the forum search here to find it. When the next Java update comes around, give it a try & if things go bad you can always reinstall the Java that works for you