Grease a 3-quart rectangular baking dish; set aside. Cook lasagna noodles in a large saucepan in a large amount of lightly salted boiling water for 10 to 12 minutes or until tender, but still firm. Drain the noodles; rinse with cold water. Drain well; set aside.
Meanwhile, place a steamer basket in a large pot. Add water to just below the bottom of the steamer basket. Bring to boiling. Add broccoli, bell pepper, zucchini, and summer squash. Reduce heat. Cover and steam for 6 to 8 minutes or until the vegetables are crisp-tender. Remove from heat.
Beat eggs in a medium bowl with a wire whisk or rotary beater. Stir in cottage cheese, ricotta cheese, basil, thyme, garlic, salt, hot pepper sauce, and ground pepper.
Layer 3 of the cooked lasagna noodles in the prepared baking dish. Spread with one-third of the ricotta cheese mixture. Top with one-third of the vegetable mixture and ⅔ cup of the mozzarella cheese. Repeat the layers twice more.
Cover the baking dish with foil and chill for at least 4 hours or up to 24 hours.
To serve, preheat oven to 375°F. Bake the lasagna, covered, for 55 to 65 minutes or until heated through. Remove from the oven. Uncover. Let stand for 10 minutes before cutting to serve.