Seriously, this! OP has a LAN with a server(s) running local services. A home lab isn’t for them and that’s fine. They obviously recognize that others like to call their local setup a home lab. At an institution, it would be called a computer lab and has been since they’ve been around. Businesses have various names (closet, colo, noc, etc.) but they’re all servers and networking infrastructure. Maybe gear is the deciding factor. A home lab would more likely use professional gear where if you’re merely self-hosting with SOHO gear, it’s just a LAN. No lab needed.