Orderby query does not work for custom fields even with meta query

I don’t believe order_clause is an acceptable orderby parameter. According to the documentation you will need to add a meta_key to your query if you want to orderby a meta_value.

I have amended your query to display attorney posts where the custom field key Last name is present regardless of the custom field value. orderby is set to meta_value which refers to the meta_key which has been set to Last name.

$connected = new WP_Query(
  array(
    'connected_type' => 'posts_to_pages',
    'connected_items' => get_queried_object(),
    'nopaging' => true,
    'post_type' => 'attorney',
    'attorney_category'=> 'partner',
    'post_status' => 'publish',
    'posts_per_page' => -1,
    'caller_get_posts'=> 1,
    'meta_key'  => 'Last name',
    'orderby' => 'meta_value title',
    'order' => 'ASC',
  )
);

Presuming your custom field is actually called Last name this query should work.

You could add a second orderby parameter such as title as a fallback:

'orderby' => 'meta_value title'