Preheat oven to 425 degrees. Spread cubed butternut squash on a large rimmed baking sheet, drizzle with olive oil, and sprinkle with salt and pepper. Stir. Roast 15 minutes, then add the shallot, garlic, and thyme and stir. Return to the oven and roast an additional 20 minute or until squash is soft.
While squash roasts, prepare the spinach filling. In a medium bowl, combine 1/2 c. milk, 1 1/2 c. ricotta, egg, chopped spinach, and 1 3/4 c. mozzarella.
Reduce oven temperature to 400 degrees. Place roasted squash mixture in a large bowl and mash until mostly smooth. Add 1/2 c. ricotta and 1/2 c. milk and stir well.
Assemble the lasagna. In an 11 x 7 baking dish, spread about 1/2 c. spinach mixture. Cover with three lasagna noodles, followed by 1/3 of the squash mixture, then 1/2 the remaining spinach mixture. Repeat with another layer of noodles, 1/3 of the squash, and the last 1/2 of spinach. Finish off with three more noodles, the last of the squash mixture, and a final sprinkle of mozzarella and Parmesan.
Cover the lasagna tightly with foil and bake 30 minutes. Remove foil and bake another 15 minutes. Let stand 10 minutes before slicing.