Heat oven to 425°F. Toss eggplant, zucchini and red onion with oil and 1/2 teaspoon salt on a large sheet pan and roast for 25 to 30 minutes, turning twice, until tender and browned with little loose liquid.
Mix tomatoes, water, garlic, oregano, remaining salt and pepper in a bowl. In another bowl, combine ricotta, egg and Parmesan.
Butter a 6-quart slow cooker and spread 3/4 cup tomato sauce over the bottom. Divide dry lasagna sheets into three groups and break them to fit without thick overlaps.
Layer one group of noodles, one-third of the ricotta mixture, one-third of the roasted vegetables, one-third of the remaining sauce and one-third of the mozzarella. Repeat twice, keeping all noodle edges covered by sauce.
Cover and cook on low for 3 to 3 1/2 hours, checking at 2 1/2 hours, until the center sheets are tender and the filling reaches 165°F.
Switch off, uncover and rest for 20 minutes. Cut into eight portions and lift with a wide spatula; the oven-ready noodles go into the cooker dry.