Adjust oven rack to middle position, place rimmed baking sheet on rack, and heat oven to 450°.
Meanwhile, toss tomatoes, eggplant, zucchini, 2 tablespoons oil, 1 teaspoon thyme, garlic, 1/2 teaspoon salt, and 1/4 teaspoon pepper together in bowl. Pat fish dry with paper towels, brush with 1 tablespoon oil, sprinkle with remaining 2 teaspoons thyme, and season with salt and pepper.
Brush remaining 1 tablespoon oil evenly over hot sheet. Spread vegetables over two-thirds of sheet, and lay fish on opposite side. Roast, stirring vegetables occasionally, until fish registers 160 degrees, about 20 minutes.
Transfer fish to platter, cover with foil, and let rest while finishing vegetables. Heat broiler. Toss vegetables with pan juices and spread out evenly over sheet. Add lemon wedges to sheet. Broil vegetables on middle rack, stirring occasionally, until vegetables are tender and slightly charred around edges, 5 to 10 minutes. Transfer vegetables to platter and sprinkle with basil. Serve fish and vegetables with roasted lemon wedges.