How to add css class to a specific set of images?

You can use the get_image_tag_class filter which passes the attachment ID as an argument:

apply_filters('get_image_tag_class', string $class, int $id, string $align, string|array $size)

So you can use:

function my_image_tag_class($class, $id, $align, $size) {
   // Logic to check your attachment IDs
   if($some_logic) {
       $class .= ' no-lazy-loaded';
   }
   return $class;
}
add_filter('get_image_tag_class','my_image_tag_class');

If you have an array of attachment IDs you want to filter, your logic would be:

if(in_array($id, $your_array_of_attachments)) { ...