Get Categories Where Taxonomy Equals 'n'

I have a custom taxonomy(the taxonomy is types) that is basically a selector that tells WordPress which section of the site to place the new post.

So for example

1. I create a new post and select Lifestyle from the custom taxonomy list.
2. Then I would select a category to place the post under, for example Healthy

I am trying to list the categories of Lifestyle in a custom menu format but only if posts exist under the taxonomy type and category selected.

What I am getting is a full list of categories but not filtered by taxonomy type.

Can anyone see where I have gone wrong?

<?php
$args=array(
  'types' => 'Lifestyle',
  'orderby' => 'name',
  'order' => 'ASC',
  'hide_empty' => 1
  );
$categories=get_categories($args);
  foreach($categories as $category) {
    if ($category->count > 0){
    echo '<li class="'.$category->slug.'"><a href="?category=' . $category->slug . '">'.$category->name.' / '.$category->count.'</a></li>';
        }
    }
?>

Thanks so much in advance!
-d