Depends on what you mean by “localhost”. Localhost is just the computer you’re currently logged in / sitting in front of… But I don’t know what kind of computer that is and how it is connected to the internet.

You’d need a webserver that is reachable from the internet to be able to have a Lemmy instance that can interact with other parts of the network. The webserver itself can run on any machine. You just need to make it accessible from the internet. So you either have a connection to the internet that allows hosting stuff… Use port forwarding in your router (at home) or if that’s all not available use a tunnel or VPN.

I really don’t know were you’re trying to get… If your question is: Can I selfhost stuff from a domestic internet connection: The answer is: Probably. Depends a bit on the provider and setup.

If your question is: Do I need a domain name? The answer is: Probably yes if your (external) IP address changes frequently.