Hi Claudio, is the “add to cart” button the one that sais “Jetzt Vorlagen herunterladen!” on your example product page? And do you want it to open the target page inside a light box?
If so, then you will have to find a way to give that button link an extra class “fancybox-iframe”. It currently has class="single_add_to_cart_button button alt" but this needs to become class="single_add_to_cart_button button alt fancybox-iframe" but it depends on your theme how.
Is that a widget area or are there options related to the button on the product edit page maybe? If you see any option to set additional classes, then please try that and let me know so I can take a look at the resulting page source 🙂