Issues with TV provider sign in on Fire TV apps is often related to problems with the Silk web browser. If the Silk browser has been removed from your device, is not up-to-date, or is otherwise problematic, this can cause issues with single sign-on TV provider functionality on Fire TV apps.
Please make sure the Silk web browser app is reinstalled and up-to-date on your Fire TV device, and then try your provider sign in again in the Lifetime app. You may need to reinstall the app or clear its cache after you have reinstalled the Silk browser.