Have you tried the fixes in the thread below?
If LW Will Not Connect

Your Java version's pretty old, so start off by updating that. Next thing to try would be deleting LW's preferences folder. Otherwise, try the rest of the fixes.

Where are you connecting from (house, appartment, school, work etc)?

Are you using a modem/router? If so, what's the brand & model number?

What options do you have ticked within LW's tools > options > advanced > firewall config (ie are you using UPnP or manual port forwarding, or do you have 'do nothing' ticked)?