Are you actually using Java 1.5 for LW? You can change which version of Java via the Java prefs setting in the Utilities folder; see Setting up Java 1.5

I'd recommend repairing permissions after a safe reboot. ie: Restart the computer whilst holding down the SHIFT key. You'll eventually see a window with the safe boot option .. choose it. Then go to Utilities folder & open Disk Utility & repair permissions. Then reboot normally & try LW again.

If that doesn't fix it then it might be worth trying to reinstall the Java 1.5 using an "Offline" installer. http://www.apple.com/downloads/macos...lease4ppc.html this one is for standard macs not the Intell one. If you have the new Intell mac, then get http://www.apple.com/downloads/macos...ase4intel.html
BTW if it won't let you reinstall it, you'll need to remove the J2SE50Release4.pkg file from the Receipts folder found in the Library folder. But ONLY remove this file. All others are required by the system!!! Then try installing it again.
(ie: Mac OSX/Library/Receipts/J2SE50Release4.pkg)

If this doesn't fix the problem, ... then it might be QuickTime. If you had QuickTime 6 on your computer before you installed QT 7 then you may need to remove all QT 6 receipts. Follow directions here http://docs.info.apple.com/article.html?artnum=301852