Replace `$parent` in `child_of` argument of `wp_list_pages` by `parent->ID`.
`wp_list_pages` needs the post id instead of post object.

    <?php 
      global $post;
      $direct_parent = $post->post_parent;
      $parent = $direct_parent->post_parent;
      wp_list_pages( array(
       'child_of' => $parent,
       'title_li'     => false,
       'depth' => 1
     ) );
    ?>