how to add the "last" class to the last menu item?

You don’t need to add a separate class.
You can select the last li like this

li:last-child {}

I know about li:last-child and it’s jQuery variant. But can i do it via “nav_menu_css_class” filter?

I’ve done this before using the following code. Just add it to your functions.php file. It doesn’t use the filter that you mentioned but it does the trick.

function add_menu_item_last_class( $items ){
   $items[count($items)]->classes[] = 'last';
   return $items;
}

add_filter('wp_nav_menu_objects', 'add_menu_item_last_class');

Another way would be to turn on CSS Classes from Screen Options on the Appearance->Menus page and then add the class manually to the required menu item.

Thank you, martinjohnharvey! This method doens’t use that filter, but uses the logic i wanted.