Live Theme Editor extension customizes the core files based on OCMOD system.

If you encounter the problem the extension can not save options, please try to go admin > Extensions > Modifications > click on the Refresh button to allow OCMOD system rebuilds modifications.

Note that if the problem is not solved, it seems that you have installed your store from auto-installer of hosting. It changes config.php file and causes OCMOD of OpenCart does not working.

You can follow this solution for fix it: