Local Brand Manager automatically authenticates with your Google Accounts upon clicking the "Add Account" button on your dashboard (https://app.localbrandmanager.com/google_accounts):

Once you click the "Add account" button, your browser will be redirected to Google and you can start the authorization process. After granting permissions to your account, you will then be redirected to your Local Brand Manager dashboard, where you can choose which locations from the Google account you'd like to sync.

There is currently no limit to the amount of Google accounts you can add to your Local Brand Manager account, it's all based on your account size.