LimeWire will not work with Java 1.7 unfortunately. The present Java 1.7 appears to be a beta version, not yet a full release version. You can still use LimeWire if you re-install Java 1.6. It is possible to still have two versions of Java on your system on Windows 7 (I tested this myself a few weeks ago.) Java control panel is where you can make decisions if you wish to disable either version if necessary.

Direct Java 6 Update 29 offline download link. Before installing, right-click the Java installer & choose to Run as Administrator. This is necessary with Windows 7 for LW to run properly. Or this link for the francais version Téléchargements Java pour tous les systèmes d'exploitation - Recommandé Version 6 Update 29