Preheat oven to 350°F. Spray a 9" × 13" baking dish with vegetable cooking spray.
Add tofu, beets (reserving juice), nutritional yeast, walnuts, miso paste, garlic powder, and basil to a food processor. Pulse until smooth. Add 3 tablespoons reserved beet juice and pulse until a spreadable consistency is achieved. Add 1 cup vegan mozzarella shreds and pulse again to combine. Set aside.
In a large bowl add pasta sauce and vegan crumbles. Stir to combine.
Pour 1 cup sauce mixture into bottom of prepared pan. Arrange 4 lasagna noodles on top of sauce. Pour 1 cup sauce mixture over noodles. Spread 1⁄2 beet filling over sauce. Repeat another layer of lasagna noodles, sauce, and filling. Finish with one more layer lasagna noodles, topped with remaining sauce. Sprinkle remaining mozzarella over top.
Tear off a piece of aluminum foil large enough to cover baking dish. Spray bottom side of foil with vegetable cooking spray. Cover baking dish with foil, crimping edges around sides of pan. Bake covered pan 45 minutes.
Use tongs to carefully remove foil and bake another 15 minutes uncovered. Remove from oven and let cool 10 minutes.
Refrigerate covered up to 5 days or freeze up to 2 months. To serve, place individual slices on a large plate and cook in microwave in 30-second intervals until heated through.