Pre heat oven to 425 degrees
Thinly slice carrots and zucchini on mandoline or with a knife.
Slice remaining vegetables with a knife. Place vegetables in a bowl and toss with mined garlic, olive oil, salt and pepper to coat. Lay vegetables in a single layer on stoneware pan or sheet pan lined with parchment paper. Roast in 425 degree over for 25 minutes.Cool thoroughly before assembling lasagna. Lower oven temperature to 350 degrees.
Prepare cheeses and set aside.
Brush olive oil in the bottom of baking dish. spoon a thin layer of marinara sauce into bottom of dish top with lasagna noodles. Sprinkle with parmesan cheese then a layer of the roasted vegetables. Top vegetable layer with sliced mozzarella cheese.
Repeat layers 2 more times. Three layers total. Cover with foil and bake at 350 degrees for 35 minutes, uncover and bake 30 minutes more until hot and bubbly.
Remove from oven and let stand 5 minutes before serving. Cut into 8 main course servings or 10 side dish servings.