Cut eggplant slices into wedges and place in a large bowl. Add zucchini, summer squash, mushrooms, tomatoes, olive oil, garlic, oregano, and salt; toss to combine. Place vegetables in a single layer in the air fryer basket, working in small batches if necessary.
Cook vegetables in the air fryer at 360 degrees F (182 degrees C) for 5 minutes. Stir, and continue to cook until tender and edges turn golden brown, about 5 minutes more. Transfer vegetables to a baking pan and place in the preheated oven to keep warm while cooking remaining vegetables.
Sprinkle vegetables with lemon zest before serving.