Heat the oven to 425°F (220°C). Arrange two racks in the middle of the oven. Line 2 rimmed baking sheets with parchment paper or aluminum foil.
Scatter the broccoli and cauliflower on one of the rimmed baking sheets. Place the peppers and zucchini on the other.
Pour half of the olive oil over each of the sheets of vegetables. Add to each pan half of the garlic powder, salt, and pepper. Toss to evenly coat, then spread the vegetables in one well-spaced layer on each of the baking sheets.
Roast the vegetables until golden brown, charred on edges, and quite tender, 20 to 25 minutes for the peppers and zucchini and 30 to 35 minutes for the broccoli and cauliflower, tossing the vegetables once or twice during cooking. Check for doneness by poking each vegetable with the tip of a paring knife; they should show very little resistance, like poking a stick of slightly softened butter. If one vegetable is done and the others need more roasting time, remove the fully cooked vegetables to a plate and continue cooking the rest.
When all the vegetables are cooked, squeeze 1/2 of a lemon over each pan of vegetables, toss, taste, and season with salt and pepper, if needed.
Transfer to a serving dish and serve warm or at room temperature.