I hope someone more knowledgeable and patient will come and provide a more detailed reply but the gist of it is that Lemmy is paid by the admins of each instance.

Lemmy is a framework, not a specific site. It allows anyone to setup an "instance" (like an individual lemmy-type site/server) and communicate to each other. If some admin has limited funds, they can limit the size of their instances to keep the costs down. If another admin has deeper pockets, , then they can make a large instance with thousands of users.
For example, the framework allows admins to limit the size of uploaded images. So a small instance can limit the size of pictures to 1 mb to save storage space and bandwidth.

Edit: As for the development of the framework itself, it's an open source project. It's built on the goodwill of volunteer developers. The lead ones are very left learning (to avoid flame war) and might keep supporting it just to throw a middle finger to the big greedy corps. They gotta eat though, so donations are certainly going to be welcome.

Edit 2: I wonder how bad the userbase would react to someone using lemmy for a setup like that of animanch.com. The admin of that site keeps a fairly active public forum that he uses to farm content to post on his monetized blog, which in turn supports the cost of said forum.