For squash filling: Heat oven to 400°. Slice ¼-inch off the top of the head of garlic, exposing cloves. Spoon ½ tablespoon of coconut oil over exposed surface and wrap the head in foil. Rub inside of each butternut squash half with ½ tablespoon coconut oil and sprinkle with sea salt. Place squash in large baking dish. Roast squash and garlic until soft, about 50 minutes. Remove both from oven, unwrap garlic, and let cool.
Scoop flesh of squash into a medium bowl. Add roasted garlic, squeezing bottom of the head to push cloves out of their paper skin and mash them together with a fork. Stir in sage and season with salt and pepper.
For spinach-onion filling: Heat 1½ tablespoons coconut oil in large skillet over medium-high heat. Add onions and cook for 4 minutes. Reduce heat to medium-low and cook until onions are soft and golden brown, about 15 minutes. Transfer to medium bowl, and set aside. Add 2 tablespoons of water and spinach to now empty skillet. Cook over high heat until spinach wilts, about 2 minutes. Drain spinach in a colander, squeezing out excess liquid. Combine spinach and onions.
For béchamel-cheese sauce: Heat 4½ cups milk in medium saucepan over medium heat until steaming hot and bubbles form along the edges. In small bowl, combine remaining ½ cup milk and flour. Whisk flour mixture into hot milk until blended. Bring to a boil, reduce heat and simmer, stirring constantly, until thickened, about 5 minutes. Remove from heat and stir in red pepper, nutmeg, 1½ cups cheese, and season with salt.
To assemble: Line 9-by-13-inch baking dish with heavy-duty, non-stick aluminum foil, allowing several inches of foil to extend over each side. Spread ½ cup of béchamel-cheese sauce on bottom of pan. Cover with layer of 3 pasta sheets. Top with half of squash mixture, then half of spinach mixture, and then 1 cup of béchamel-cheese sauce. Repeat layers: pasta, squash, spinach, béchamel. Top with remaining pasta sheets. Spread remaining béchamel-cheese sauce over pasta and top with remaining ½ cup cheese.
To freeze/bake: Freeze unbaked lasagna until firm. Lift from baking dish by holding edges of foil. Fold foil ends over lasagna. Wrap lasagna in additional foil, sealing it tightly. Freeze for up to 1 month.
Remove lasagna from foil and place on lightly-greased 9-by-13-inch baking dish. Cover and thaw overnight in refrigerator.
Heat oven to 425°. Bake, uncovered, for 30 minutes. (If baking the lasagna frozen, plan to double the baking time.) Allow to sit for 10 minutes before serving.