I host a lot of software internally on my home network too but I didn't want to run Lemmy from my home so I host it in AWS which is not particularly cost-effective. The bulk of the cost is from the vps. I'm not paying on-demand pricing but it's still more expensive than I'd like. I also pay for a static IPv4 address, object storage (for the image hosting) and like you mentioned before, the domain. It's roughly $30 per month although that cost has a small overlap with another service I run on the same vps.
I might start hosting Lemmy locally too at some point mostly to cut costs. I'd like to isolate my more internet-facing software like Lemmy to a separate LAN isolated from the rest of my home network. I have a few things at home exposed to the internet through a reverse proxy right now but with Lemmy being very open and public by it's nature I don't want it mixed in with the rest of my network so I'll probably buy a small block of IPv4 addresses from my ISP before I move it.