If the LW program can run but will not connect. Some things you could try such as changing ports.

Go to LW's menu bar, Tools -> Options -> Advanced -> Firewalls, change both listening & connection ports to one of the following: 80, 443, 427, 1111, or one between 49152 - 65535. Port 80 is what browsers use so it will not be blocked but might be reserved. Ports 427 & 427 I think are iTunes ports from memory. The highest ports are ones that are not reserved for specific purposes & are usually the last that isp's block.

However no doubt there will be a software firewall on the computer you will not have access to in order to allow LW full access. The library's router might also be an issue, not to mention their security systems.