Preheat the oven to 350°F (175°C) and grease a 9x13-inch baking dish.
Bring a large pot of salted water to a boil, add 1 tablespoon olive oil, and 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 the crushed red chili, ground pepper, dried Italian seasonings, 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 coated, about 5–7 minutes; remove from heat.
In a medium bowl, combine the ricotta cheese, eggs, a pinch of salt, and a little ground pepper until smooth.
Spoon about 1/4 cup of the vegetable sauce into the bottom of the prepared baking dish to lightly coat it.
Arrange a layer of cooked lasagna noodles over the sauce. Spread one third of the vegetable sauce over the noodles, then dollop and spread half of the ricotta mixture evenly over the sauce. Sprinkle with some Parmesan and mozzarella.
Add another layer of noodles and repeat: one third of the vegetable sauce, the remaining ricotta mixture, and more Parmesan and mozzarella.
Top with a final layer of noodles, the remaining vegetable sauce, and the remaining Parmesan and mozzarella cheese.
Cover the dish with aluminum foil and bake at 350°F for 20 minutes. Remove the foil and bake for an additional 15 minutes.
Broil for 2 minutes until the top is golden and bubbly, watching carefully to avoid burning. Let rest a few minutes, then slice and serve warm.