Here's what I have concerning this. LW only gives that problem when it detects NO connection to the net. Be it that there has been a slight break on DSL (which happens), or you disconnect your modem.
With modems, even if you select "disconnect" in the LW menu before disconnecting the modem, that's the only time CPU usage goes up, and from there onwards, it stays up. Restoring a connection to the net doesn't help. LW will reconnect and work like normal, but it will keep using CPU resources until the program is shut down and restarted.
If there's no break in your connection to the net, (modem that has never been disconnected with LW being started after making the net connection, or if you have an EXTREMELY GOOD DSL connection) LW works beautifully. but the instant it can't detect a net connection, even if for a split second (DSL too), CPU usage goes up through the roof, and stays there. It seems like a bug in LW and not Java.

that's my 2 cents. I'm sure if you look closely at LW you'll notice this too.