Steam – TF2 dedicated LAN server not found in game’s server browser

If it's only people on the same LAN that can connect, then the problem is almost definitely to do with the server's firewall or, more likely, the router that your friend is using.

In the first case, it may be that the firewall is configured to accept connections from computers on the same subnet (i.e. on the LAN), but block connections coming from computers outside the subnet. Set the firewall permissions on the server, and you're set.

In the second case, it's likely that the ports used by the server aren't being forwarded by the router. The router doesn't know what to do with incoming connections that weren't initiated by one of the computers on the LAN, and the TF2 server might not be smart enough to tell the router that it's listening on port 270xx. Forward the required ports using the router (web) configuration tool, and you should be good to go.

Here is some more information about setting up a server, and the needed ports.

EDIT: @Matthew Read posted a nice answer on a similar question listing the ports in use by Valve games.

This shouldn't happen. But there are tutorials online to make a legit local server. But instead you could make a online server with a password. Then it would be a private server for your friends.