I'm not sure how to fix it yet, but here's what's been happening to me:

Recently, I'll start LW and there's a brick wall in front of the globe (showing that I have a firewall problem).

I've been using LW for a while now, and I've never had any firewall issues. I have my McAfee firewall configured to allow LW access to the internet, and I have my Windows XP firewall turned off.

After a few minutes, however, the brick wall disappears and I'm back to downloading as usual...

Try some magnet links from Bitzi to see if they work. Was the firewall icon always there?

Also getting rid of the firewalled icon might help. Most likely the firewall being picked up is in your router.

www.portforward.com has guides on how to do this for many routers.