Preheat the oven to 350°F (175°C) and grease a 9x13-inch baking dish with a little olive oil or cooking spray.
Bring a large pot of salted water to a boil; add 1 tablespoon olive oil and the lasagna noodles and cook according to package directions until al dente. Drain and set aside separated so they do not stick.
Heat the remaining olive oil in a large skillet over medium heat. Add the chopped onion and cook until translucent, about 3–4 minutes, then add the minced garlic and cook 30 seconds more.
Add the chopped carrots, red bell pepper, and zucchini to the skillet and cook 4–5 minutes until slightly softened.
Stir in the crushed red chili, black pepper, dried Italian seasoning, chopped basil, and salt to taste.
Pour in the crushed tomatoes and simmer on medium-low until the sauce thickens and the vegetables are well combined, about 5–7 minutes. Remove from heat.
In a medium bowl, mix the ricotta cheese with the eggs and a pinch of salt and pepper 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. Spread one-third of the vegetable sauce over the noodles, then half of the ricotta mixture, and sprinkle with some Parmesan and mozzarella.
Repeat the layering: noodles, another third of the vegetable sauce, the remaining ricotta mixture, and more Parmesan and mozzarella; then add a final noodle layer, remaining vegetable sauce, and top with the remaining cheeses.
Cover the dish tightly with aluminum foil and bake at 350°F (175°C) for 20 minutes.
Remove the foil and bake uncovered for an additional 15 minutes, then broil for 2 minutes until the top is golden and bubbly—watch closely while broiling.
Let the lasagna rest 5–10 minutes before slicing and serving warm.