Grain free Starch free Lasagne

I know a lot of you are trying to go dairy free, but I have no idea how to make dairy free lasagne! I mean, cheese is the very essence of this amazing dish!! But it doesn't have any noodles, thanks to squash, so I hope it'll work for some of you! :)
Lasagne
2 lbs. Hamburger
1 Onion chopped
1 Tbsp. Minced Garlic
15oz. Tomato Sauce
15oz. Diced Tomatoes
2 Tbsp. Italian Seasoning
1 Tbsp. Dried Basil
3 Yellow Squash
3 Zucchini
2 lbs. Cottage Cheese
1 Cup Parmesan
2 Eggs
1 Tbsp. Dried Parsley
2 1/2 Cups Mozzarella
1 tsp. Salt
1 tsp. Pepper
Brown hamburger with onions and garlic, add diced tomatoes, sauce, and Italian and basil seasonings. Let that mixture simmer while you slice the squashes. Mix together cottage cheese, Parmesan, eggs, parsley, salt, pepper, and 1 cup mozzarella.
Layer half the squash in a 9x13 pan, scoop half the meat sauce over the squash, and half the cheese mixture over sauce. Repeat layers, top with remaining 1 1/2 cups of mozzarella. Bake at 350 uncovered, for 30-45 minutes, or until brown and bubbly all the way through.
You might notice the sauce is less juicy than normal lasagne, this is because squash gets so watery when you cook it, that you have to leave out some tomato sauce, so your dish won't be completely runny!
You could make this dairy free, by leaving out the cheese, and it would taste good, but it wouldn't be lasagne! It would be more like ratatouille, with meat....and ratatouille doesn't have meat...but it is quite delicious, and I will make it for you sometime!