I don't know what the problem is with you guys my every time I start up LW it takes only a few millieseconds to connect.
things you should check:

>Are you running the right MRJ?-> If not: download from the official apple website.

>Are you trying to connect to a specific group (adult, audio, Asia, ...)?-> If so: don't / If not: try.

>If really nothing works: uninstall and try again. Don't worry, you won't loose your shared and incomplete files. Some good advise (it worked for me so why not for you?) : Before you (re-)download LW go to the offical apple website and download the right MacOs Runtime Java (MRJ). LW normally does this for you before you download the actual app itself but I think that this is the problem.