Getting taxonomy terms used by custom post type

If you see doc for wp_list_categories in codex, you’ll se that it accepts a include param, that should contain a comma separed list of categorys ids.

So if you change your function get_terms_by_post_type creating the function get_terms_id_by_post_type to retrieve only the term ids, just like:

function get_terms_id_by_post_type( $taxonomies, $post_types ) {
    global $wpdb;
    $query = $wpdb->get_col( "SELECT t.term_id from $wpdb->terms AS t INNER JOIN $wpdb->term_taxonomy AS tt ON t.term_id = tt.term_id INNER JOIN $wpdb->term_relationships AS r ON r.term_taxonomy_id = tt.term_taxonomy_id INNER JOIN $wpdb->posts AS p ON p.ID = r.object_id WHERE p.post_type IN('" . join( "', '", $post_types ) . "') AND tt.taxonomy IN('" . join( "', '", $taxonomies ) . "') GROUP BY t.term_id");
    return $query;
}

Then you can:

// retrieve the term ids used by post type
$terms = get_terms_id_by_post_type( array($tax), array('case') );

// if that terms exist implode in a commasepared string
$term_list = ! empty($terms) ? implode(',', $terms) : false;

// use wp_list_categories with include param to included only used terms
if ( $term_list ) {
  wp_list_categories(
    array(
        'taxonomy' => 'antibiotic_types',
        'hierarchical' => 1,
        'hide_empty' => 1,
        'title_li' => '',
        'include' => $term_list
    )
  );
}