Preheat the oven to 350°F (175°C) and lightly grease a 9x13-inch baking dish.
Bring a large pot of salted water to a boil with 1 tablespoon oil; cook the lasagna noodles according to package directions until al dente, drain, and set aside.
Heat the remaining 2 tablespoons olive oil in a large skillet over medium heat; add the chopped onion and minced garlic and cook until the onion is translucent, about 3–4 minutes.
Add the chopped carrots, red bell pepper, and zucchini to the skillet and cook for 4–5 minutes until slightly softened.
Stir in crushed red chili flakes, ground black pepper, dried Italian seasoning, chopped basil, and salt to taste.
Add the crushed tomatoes, reduce heat to medium-low, and simmer until the sauce thickens and the vegetables are well combined, about 5–7 minutes; remove from heat.
In a mixing bowl, combine the ricotta, eggs, and a pinch of salt and pepper; stir until smooth.
Spoon about 1/4 cup of the vegetable tomato sauce into the bottom of the prepared baking dish and spread evenly.
Arrange a layer of cooked lasagna noodles over the sauce, then spread one-third of the remaining vegetable sauce over the noodles, followed by half of the ricotta mixture, and sprinkle with some Parmesan and mozzarella.
Repeat the layering: noodles, one-third of the vegetable sauce, the remaining ricotta mixture, and more Parmesan and mozzarella; finish with a final noodle layer, the remaining sauce, and the remaining cheeses on top.
Cover the baking dish with aluminum foil and bake at 350°F (175°C) for 20 minutes; remove the foil and bake for an additional 15 minutes.
Optional: broil for 1–2 minutes until the top is golden and bubbly, watching closely to prevent burning.
Let the lasagna rest for 5–10 minutes, slice, and serve warm.
