Place eggplant in large colander set over sink; toss with 1 tsp. salt. Let it sit and drain for 15 - 30 minutes. Add zucchini and remaining 1 tsp. salt; toss. Drain 30 more minutes, tossing occasionally.
Rinse vegetables thoroughly under cold water and drain. Then squeeze out excess moisture, working in batches if necessary. Transfer vegetables to 5- or 6-quart slow-cooker.
Dice 1 tomato. Add diced tomato, garlic, onion, bell pepper, water, and black pepper to slow-cooker; stir to mix. Cover and cook until vegetables are fork-tender, about 3 hours on low. Stir in vinegar and thyme.
Transfer mixture to a bowl. Cover and refrigerate until completely chilled, at least 4 hours or overnight.
Dice remaining tomato. Line platter with lettuce, top with eggplant mixture. Serve, sprinkled with tomato.