Dockerhub Automatic Build with Github LFS
There is nothing regarding lfs in docker/hub-feedback.
Nor is there anything in docker/notary or docker/docs.docker.com, or docker/distribution
The Docker Hub Automatic build "allow[s] you to use Docker Hub’s build clusters to automatically create images from a GitHub or Bitbucket repository containing a Dockerfile".
Since Git LFS is only official on GitHub repos is only official for the last 14 days, and being worked on for BitBucket (coming from their original Git LOB initiative), it seems safe to say LFS isn't yet supported by an Automatic build.
Update June 2016, Andy Li reports in the comments below:
There is now a feature request issue in docker/hub-feedback:
Issue 500: "Add support for Git LFS".
It needs your support (or your Pull-Requests)
4 years later, Q4 2019, you might consider as an alternative GitHub Actions. Check this other question for more details on how to use git-lfs in them.