You are not reading content from lemmy.dbzer0.com unless you specifically have only that at the beginning of the address. If you have lemmy.world instead, it means you are trying to view content cached there, which no longer exists.

It is relatively light on resources, you can even host it on your own PC. And it does not need to be public, just don’t expose the port publicly and voila…

You can do it totally anonymously, you just need a server with docker that can’t be linked to you. There are many ways (legal or not) to acquire such server, and afterwards it’s simple.