You may still want to remember that the visitor/member is working in the session that they have ‘logged into’. So for example if they log in and you remove the lightbox and the user refreshes the page in the browser then the lightbox will return and they will be asked to log in again. If that is what you want them to do then your outline above seems reasonable. If it isn’t then you need to use wix-storage to remember that they have logged in and effectively log them in behind the scenes and don’t show the login light box again.
Hope that makes sense.