Use search in fancybox

The easiest way:

1. create a page template that only includes the search form (get_search_form())
2. create a page and assing the template
3. In the href attrib of the iframe, instead of put the url for searchform.php put the url of the page

Pretty easy, but you need a query to get the page. A more performant way is to use fancybox without iframe, but via ajax, e. g.:

<?php
$url = add_query_arg( array('action'=>'show_search_form'), admin_url('admin-ajax.php') );
?>
<a id="search-label" href="https://wordpress.stackexchange.com/questions/153098/<?php echo $url; ?>"></a>

Then use ajax API to call get_search_form() inside the ajax action, e. g.:

add_action( 'wp_ajax_show_search_form', 'mytheme_show_search_form' );
add_action( 'wp_ajax_nopriv_show_search_form', 'mytheme_show_search_form' );

function mytheme_show_search_form() {
   get_search_form();
   exit();
}