Git Large File Storage (LFS) replaces large files such as audio samples, videos, datasets, and graphics with text pointers inside Git, while storing the file contents on a remote server.
With Git LFS 2.0.0 you can now lock files that you're actively working on, preventing others from pushing to the Git LFS server until you unlock the files again.
This will prevent merge conflicts as well as lost work on non-mergeable files at the filesystem level. While it may seem to contradict the distributed and parallel nature of Git, file locking is an important part of many software development workflows particularly for larger teams working with binary assets.
What I'm thinking is not only a visual representation on your website GUI but also some front-end functionality on SourceTree such as the currently implemented SourceTree Git LFS warning that XYZ file(S) are larger than 2MB.
I'd look to GitLab's iteration for guidance: https://docs.gitlab.com/ee/user/project/file_lock.html