I have been told that an [Ed]Ubuntu LTSP Server has no open ports by default and so does not need a firewall, and that a firewall will not only make installation more difficult but the LTSP community may also be unable or unwilling to assist with troubleshooting. But they also say that the "clients must not be connected to a routable interface".

Is there any way that my LAN, connected to the internet by a router with NAT firewall, could be inadvertantly made routable?

What sorts of services could I run, or devices could I connect, for example, to make it routable?

As for the server side it certainly looks to me that a typical LTSP terminal server has many ports open.

http://wiki.ltsp.org/twiki/bin/view/Ltsp/LtspPorts

On the other hand the clients in a private network may very well not need a firewall.

The need for a firewall would be dependent on your network architecture and how the LTSP server was being used and where the LTSP server was placed. I think by routable they mean an interface with a Public IP address, though the use of the term "routable" would be debatable.