Cook the lasagna noodles as per package instructions. Drain and keep.
To make the marinara sauce:
Heat the oil in a heavy bottomed pan. Add the garlic and onions and saute well. Add the tomatoes, salt and pepper and simmer for about 30 mins or so.
To make the squash filling:
Cook the squash in the microwave with enough water to cover it fully, until it is soft. Drain the water and keep aside.
Heat the oil and add the onions and garlic to it. Sauté until onions are translucent.
Add the spinach and once it wilts, add the cooked squash to it along with salt and pepper. Mix well Remove from heat and keep aside.
To make the cheese spread:
Combine all the ingredients in a bowl and mix with a fork until well combined.
Preheat the oven to 375F.
In a lasagna pan, spray some cooking spray on all sides.
Spread ¼ of the marinara sauce at the bottom. Arrange three lasagna sheets. Spread a ½ of the squash mixture over it. Spread ½ of the cheese mixture over the squash mixture. Pour ¼ of the marinara sauce over it and layer with three more lasagna sheets.
Repeat with the rest and end with the last set of lasagna sheets. (You will have one extra, that is ok, it was just in case one of your other sheets tore)
Top with the remaining marinara sauce and the 1 cup of grated parmesan cheese. Cover with aluminum foil. Bake covered with foil for about 30 mins or so.
Remove foil and bake again for another 15 mins or so.
The unbaked lasagna can be frozen. Thaw to room temperature before baking.