I added a binary file to my git repo by accident. If I start tracking it right now with git-lfs, will it be removed from the git history?
No Git LFS does not remove files from your git history.
After you remove files from Git LFS, the Git LFS objects still exist on the remote storage and will continue to count toward your Git LFS storage quota.
To remove Git LFS objects from a repository, delete and recreate the repository. When you delete a repository, any associated issues, stars, and forks are also deleted.
For more information, see "Deleting a repository."