Begin by making the marinara sauce. Place herbs, garlic, onion, and carrot in a food processor and process until chopped.
Heat oil in a heavy bottom saucepan over medium high heat. Transfer herb/vegetable mixture to saucepan and saute for 5 minutes. Add tomatoes, sugar, salt, black pepper, and red pepper flakes. Stir to combine. Bring to a simmer, then continue cooking for 30 minutes, stirring occasionally.
Preheat oven to 375 degrees F.
Steam carrots, zucchini, yellow squash, and mushroom for 5 minutes, or until tender. Mix with marinara sauce.
In a mixing bowl, combine ricotta, shredded mozzarella, 1 cup parmesan, and basil. Stir to combine.
Arrange the thinly sliced zucchini over paper towels. Sprinkle with salt and set aside.
Assemble lasagna by spreading 1/2 cup marinara/vegetable mixture over bottom of a 9 x 13 -inch baking dish. Cover with a layer of noodles, arranging crosswise. Spread 1/4 of the cheese mixture over noodles, then top with 1 cup sauce. Repeat 3 more times. Spread any remaining sauce over.
Pat down thinly sliced zucchini slices to remove any excess water. Arrange in a lattice pattern over lasagna. Sprinkle with 1/4 cup parmesan.
Bake lasagna uncovered with for 50 minutes to 1 hour. Let stand 15 to 20 minutes and serve.