UPDATE:

I figured it out!!

Here's how I did it. I hope this helps someone:

Find this line of code:

<?php require($template->get_template_dir('tpl_drop_menu.php',DIR_WS_TEMPLATE, $current_page_base,'common'). '/tpl_drop_menu.php');?>

For my apple zen cart I found it in includes/templates/apple_zen/common/tpl_main_page.php

Then add <div class="zenLightboxHideMe"> before it and </div> after it.

So your final code should look like this:

<div class="zenLightboxHideMe"><?php require($template->get_template_dir('tpl_drop_menu.php',DIR_WS_TEMPLATE, $current_page_base,'common'). '/tpl_drop_menu.php');?></div>

You can also change the class name for lightboxes to hide stuff in Admin-Configuration-Zen Lightbox