It's purely donation driven and he pulls a small salary from whatever's leftover after buying enough servers to keep the site up.
( link came from here https://en.lichess.org/patron )
Its source code is also really interesting, it makes me want to learn Scala.
It's been around at least as far back as 2010. Here is a 6 year old HN submission about it: https://news.ycombinator.com/item?id=1927188