That depends upon what type of blocking they're applying. They might be blocking ports, or specifically the program or ...
See these links: 1. Connection problems? Check here first!

2. You could try changing the port LW uses. Go to LW's prefs (command & comma) > Advanced > Firewalls & change both the connection & listening ports to another. Here's some to try: 1111, 64049, 3500, 4008, 1203, 10000, 15189, 80, 20282, 22817, 443, 427, 34599, 40475.
But you'd also need to change the OSX firewall port setting also ... or temporarily turn off the firewall whilst you're trying different ports. After changing a port, you'll need to apply it. Make sure LW is disconnected & go to LW menu bar, File>Connect. Give each one at least 15 mins to try to connect.

3. A Fix for those whose ISP's block Limewire pages 1 - 3 which have links to alternative instructions.