How to change the lang=”en-US” value of the HTML document?

The value for that string is normally taken from the option WPLANG in your database table $prefix_options. You can set it in the backend under Settings/General (wp-admin/options-general.php) or per SQL.

There several ways to change that value per PHP:

1. Create a global variable $locale in your wp-config.php:

   $locale="en_GB";
   

2. Declare the constant WPLANG in your wp-config.php:

   define( 'WPLANG', 'en_GB' );
   

   This has been deprecated, but it’ll still work.

3. Filter locale:

   add_filter( 'locale', function() {
       return 'en_GB';
   });
   

   This a very flexible way, because you can add more conditions to that function, for example check the current site ID in a multisite.