So, to start this interesting process, (which I am sure would be handy for hosting that dinner party where you really want to impress and make everyone ooh- and ahh over your dishwasher cooking prowess!... I guess it could also come in handy when that darned oven goes out too, but it is much more fun for previously mentioned dinner party!) I would most definitely do everything I can to clean that filter / tray in the bottom of the dishwasher out REALLY good before going ahead with the unthinkable.
According to the recipe on the site, it really is no different than any other lasagna recipe other than replacing fresh onions with onion flakes to make sure and reduce any extra water that might accumulate in your pasta dish, so use your favorite lasagna recipe and follow the directions below for an amazing dinner via DISHWASHER!!
*** I just think I will bypass on the whole clean while you cook thing though! LOL!***