Grilled vegetables: Preheat the BBQ to medium-high heat. Toss the vegetables in the oil, and season with salt and pepper. Grill vegetables on all sides. Set aside in a bowl.
Ricotta: Combine all the ingredients in a bowl. Season and stir well. Set aside.
Lasagna: Preheat the oven to 230°C (450°F). Assemble the lasagna: Start by spreading a thin layer of marinara sauce on the bottom of a 9 in. x 13 in. (23 cm x 33 cm) rectangular baking dish. Cover with lasagna noodles. Top the noodles with the ricotta mixture and overlap with half of the grilled vegetables. Spread another layer of marinara sauce over top. Cover with the remaining lasagna noodles, marinara sauce, and grilled vegetables. Garnish with tomato slices and sprinkle with parmesan cheese. Bake in the oven for approximately 30 minutes, or until mixture bubbles and top is golden.
Remove from the oven and garnish with fresh mozzarella and basil.