The mtime of the files in my working copy change when I amend or rebase or checkout different branches or in general when I use git commands. I carefully store the mtime when these files are generated or overwritten and restore it when it is going to be read. The tool I use is https://packages.ubuntu.com/bionic/metastore and does not have stale information.
I do not know how git lfs will work here, it handles large contents but I doubt it will handle the mtimes as I need.
