Store git-lfs files locally instead of pushing to server on git push

Question

So I want to store large files from a git repository (which is setup to use git-lfs) locally on a backup hard drive instead of pushing the large files to and storing them in a remote server which git lfs does by default. I basically want that backup hard drive to act as the remote server that git lfs uploads to by default.

I have tried doing this:

git config lfs.storage /absolute/path/to/local/storage

However, when I push changes to the remote repository it seems to be trying to upload the large files managed by git-lfs to a remote server, and I get this error:

batch response: This repository is over its data quota. Account responsible for LFS bandwidth should purchase more data packs to restore access.

failed to push some refs to 'https://github.com/user/repoGitLTF.git'

I am not trying to upload the large files to the remote server, just save them locally on the backup hard drive (which is not the same location as the local repository), but otherwise push all other changes to the github remote repository.

Any ideas on how to achieve this?