This is what I did to make ZoneAlarm let LimeWire access the internet and server.

#1: Allow LimeWire permission to access the internet and server by opening ZoneAlarm and clicking the Program Control tab, then scrolling to where you see LimeWire and checking the boxes. If you have done this already skip this step.

#2: Click on the tab marked Firewall.

#3: Under where the Trusted Zone Security slider is, click the button marked Advanced.

#4: Check the boxes that say:
Allow Outgoing DNS/DHCP in Trusted Zone on High setting
Allow Outgoing DNS/DHCP in Internet Zone on High setting
Allow uncommon protocols at high security

#5: Click ok.

#6: If LimeWire is open, disconnect it by going to File & hitting Disconnect. Then click Connect. At that point you may get a message saying ZA blocked something. Click ok.

The connection lights should completely light up within a few minutes depending on your connection speed.

Also note that if LimeWire cannot connect the next time you boot up, disconnect and reconnect and it should be fine until you log off again. I have to disconnect it and reconnect it once after I boot up.