They do have a reference implementation of the serverside here: https://github.com/github/lfs-test-server - though they themselves don't consider it production ready. But I'm sure it'll either get there in time, or another open source implementation will rise to the challenge (cf. syste's comment about GitLab planning support for this: https://news.ycombinator.com/item?id=10313495 )
I have data that belongs to my source, but is rather big and I want it inside of my repo.