the login button still says login (instead of logout) even after logging in…
That is probably a simple case of the page itself needing to be refreshed after the user has logged themselves in.
If you move the user onto another page then it wouldn’t be noticed as when the new page loads it will show user logged in etc.
This is a common issue with an example like the Wix Members Profile tutorial, that tells you to move the user onto their member profile page after logging in.
However, if you simply stay on the same page and just close your login lightbox, then the login button value on the page will not change from login to logout etc as the code needs to be run again if you stay on the same page after logged in.
That is why you simply need to close login lightbox and refresh page after member logs in.