Preheat oven to 375*
Lightly oil the bottom of a casserole dish then spread with about 1/3 cup of marinara. Top with 3 sheets of lasagne, side-by-side.
Spread about 1 cup of mashed squash on top, then sprinkle with mozzarella cheese. Spread about 1/4 cup marinara over this. Top with 3 sheets lasagne.
For the next layer, spread 2/3 cup of ricotta and half the spinach over the noodles. Sprinkle with mozzarella, then spread 1/4 cup marinara over all. Top with three more sheets of lasagne.
Repeat one more squash layer and one more spinach-ricotta layer.
Add the last three noodles then spread remaining marinara over all. Sprinkle with remaining mozzarella, then grated parmigiana.
Cover with foil and bake for 25 minutes. Remove foil and bake for another 5-10 minutes. Let rest 15 minutes before serving.