FYI: Example.com is called domain and Lemmy would be called a subdomain in that case…

Sorry I don’t know the answer to your question

What you’re trying to do is often called “domain delegation” or “well-known delegation”. Here’s an example of the documentation for the same thing in matrix-synapse. I don’t know if the Lemmy server supports this yet, my suggestion would be to join the matrix chat for the development and ask there. You should find a link to the chat room on the github page. If it does support it then most likely the process is the same as the one I linked for matrix.