Get SEF path of an article from external script using articleID

Question

I am practically new to Joomla and I need to get the SEF path of an article from an external php script. I feel like I'm close but something is not working for me. The preliminary code I have as an example is:

    require_once ( JPATH_BASE .DS.'includes'.DS.'defines.php' );
    require_once ( JPATH_BASE .DS.'includes'.DS.'framework.php' );
    $mainframe = JFactory::getApplication('site');
    $mainframe->initialise();

    $articleId=80;

    $url = JRoute::_("index.php?option=com_content&view=article&id=".$articleId);

With this, JRoute returns the path /component/content/article?Id=80&Itemid=437. After doing some research, I read that I must include the "itemId" of the menu. I'm not sure if it's the "437" that the JRoute returns to me, or if I should get it separately. Based on my reading, one way to get the menu item id is:

$link = 'index.php?option=com_content&view=article&id='.$articleId ;
$menu = $mainframe->getMenu();
$menuItem = $menu->getItems( 'link', $link, true );
$Itemid = $menuItem->id;

However the $Itemid returns empty. I appreciate if someone could guide me with this. What I need is to build the SEF path of the article, regardless of its menu structure. My final need is to create a link to that article based on its articleID from an external php script.