Can’t find where to modify attrbitutes

If you can’t edit your header.php, or would prefer not to, most decent WordPress themes should have (and certainly any that pass theme review to be in the official repository)

<html <?php language_attributes();?> >

in the opening html tag in the header.php template.

There is a filter in the language_attributes() function that allows plugins/child themes to modify the ouput, like so:

function wpa89133( $output ) {
    $output .= ' myprop1="val1" myprop2="val2"';
    return $output;
}
add_filter( 'language_attributes', 'wpa89133' );