Walker class conditional based on parent menu item label or custom css class

I'm out of my shallow depth here. I'm trying to add html to the end of drop down menus whose parent item is either a specific item label or custom css class that's been added via the WP menu admin.

Any help appreciated. The basics:

public function end_lvl(  $output, $depth = 0, $args = null ) {
    parent::end_lvl( $output, $depth, $args );
    if (/* top-level parent item has [specified label] or [specified css class] */){
       $output .= 'divSee how we can help you a href=#Find out more/a/div';
    }
}