Lobby games are also just lan games in essence, the only difference is that the needed address gets passed to others via a neat ui. The lobby also adds some mechanisms to allow some additional network setups to work, like firewall puching / stun. As a bonus you get a chat and a ranking bot. I'm pretty sure you don't want to setup your own lobby but you could, the code and instructions is at https://github.com/0ad/lobby-infrastructure
If you create a lan game it means 0ad on your computer will listen on the specified port for connections. Everyone around the globe that can connect to you computer will be able to join that game. How to make your computer reachable from the internet typically means adding portforwarding to your router and configuring the firewall. But even then, due to IP4 starvation your ISP might make it virtually impossible to get it working.