Preheat oven to 350°F. Spread thin layer of sauce over bottom of 13 x 9-inch glass or ceramic baking pan. Top with layer of 3 or 4 lasagna noodles. Gently spread one-third of the mashed tofu over noodles, then top with one-third of the remaining sauce.
Sprinkle about one-third of the vegetables over sauce, then top with one-third of the cheese. Repeat layering twice, beginning with noodles and ending with cheese.
Cover with foil and bake until noodles are tender, 35 to 40 minutes. If desired, uncover and continue baking until cheese is golden, about 5 minutes. Remove from oven and let stand 5 minutes before serving.