I have a project in GitHub working with git config:
git config --global user.email = "firstname.lastname@example.org"
git config --global user.name = "abc"
my email account is "email@example.com"
For your new repo, all you need to do is, in the repo folder, to do:
git config user.email = "firstname.lastname@example.org"
The local configuration will override the global one, and your commits will have the right email.
Note: this has nothing to do with the authentication on GitLab.