Sort author list alphabetically

Your Query gets the authors ID and is you want them sorted Alphabetically you will need to get the author(user object) so try:

$authors = $wpdb->get_results('SELECT DISTINCT post_author FROM '.$wpdb->posts);
if($authors){
    $users = get_users( array(
        'include' => $authors,
        'orderby' =>  'display_name'
    ));
    foreach ((array)$users as $user) {
       echo '<li>' . $user->display_name. '</li>';
    }
}