Logout hyperlink within a sub-menu

Not tested, but it might work, use wp_logout_url() wordpress in built function to get logout url.

// Add a Login hyperlink to the secondary navigation menu if the user is logged-out
function wpa_remove_menu_item( $items, $menu, $args ) {
    if( is_admin() || ! is_user_logged_in() ) return $items;

    foreach ( $items as $key => $item ) {
        if ( 'Login / Register' == $item->title ) unset( $items[$key] );
        if ( 'Logout' == $item->title ){$items[$key]->url=wp_logout_url();}
    }

    return $items;
}

add_filter( 'wp_get_nav_menu_items', 'wpa_remove_menu_item', 10, 3 );