Just to clarify:
Your copy of LW is unresponsive, i.e., you click on something and it doesn't immediately respond? Or, does the graphics user-interface (GUI) respond fine, but the program is slow to locate a connection?

Do you have the Connections window enabled? That's a good way to see what the program is doing on the network.

Did you uninstall the previous version(s) of Java before installing the new? If not, there might be multiple versions installed.

Is there a way to check which version of Java is in-use by Limewire? It should be easy enough to add in the Statistics screen, shouldn't it?