get_terms() parent, child and grandchild

Since this is for a taxonomy archive, you can just use get_queried_object() and the parent and depth argument in wp_list_categories():

$term = get_queried_object();
$list = wp_list_categories( array(
    'orderby'  => 'name',
    'taxonomy' => $term->taxonomy,
    'parent'   => $term->term_id,
    'title_li' => '',
    'depth'    => 1,
    'echo'     => false,
));

if ( $list ) {
    echo "<ul>$list</ul>";
} else {
    // Nothing, do something else!
}

Note that wp_list_categories() does not output/return a containing <ul />, so you need to do so yourself (as demonstrated).