Veggies: Heat oil in a large saute pan over medium heat. Add garlic, eggplant, zucchini, and pepper, cooking until zucchini is. slightly soft, about 3 to 5 minutes. Add spinach and cook, stirring constantly, until wilted down, about 1 minute.
Bechamel: Heat milk in the microwave for about 2 minutes, just until warm. Melt the butter in a heavy-bottomed pan over medium heat. Whisk in the flour, cooking and stirring until the mixture is slightly golden brown and no longer smells like raw flour. Slowly whisk in all of the milk, stirring well to evenly combine. Bring the mixture to a simmer and cook until thicken, about 5 minutes. Remove from heat and stir in parmesan, salt, and pepper.
Assemble: Preheat oven to 350°F (175°C). Spread ½ cup of marinara onto the bottom of a 9x9 inch casserole dish. Layer on ⅓ of the lasagna noodles, snapping some to size as needed to fit into your pan. Then layer - ⅓ of the bechamel, half of the veggies, ⅓ of the cheese, and 1 cup of tomato sauce. Top with ⅓ of the lasagna noodles.Repeat for the second layer - ⅓ of the bechamel, second half of the veggies, ⅓ of the cheese, and 1 cup of tomato sauce. Top with ⅓ of the lasagna noodles.For top - Spoon on remaining bechamel, remaining tomato sauce, and sprinkle on remaining cheese.
Bake: Covered tightly with aluminum foil, for 35 to 45 minutes, or until bubbling at the edges. If desired, remove foil and broil for 2 to 3 minutes, until the top is golden brown.