1
Adjust the oven racks in the center and bottom third and preheat the oven to 450 degrees. Line 2 large rimmed baking sheets with foil and spray with oil.
2
Slice 1 of the lemons into 1/4" thick slices. Cut the second lemon in half.
3
In a large bowl, combine the chicken, potatoes, carrots, juice from 1/2 lemon, the olive oil, 3 teaspoons of the oregano, 1 teaspoon of the salt, the garlic powder, and pepper to taste and toss well, using your hands so everything is evenly coated. Spread out in a single layer along with the lemon slices, without overcrowding, onto the prepared baking sheets.
4
Roast until the bottoms of the potatoes are golden, about 14 minutes. Flip the potatoes and carrots, switch the baking sheets from rack to rack, and roast until the vegetables are tender, the potatoes are golden and the chicken is cooked through, 14 more minutes.
5
Squeeze the remaining 1/2 lemon over everything, then top with grated feta, lemon zest, the remaining 1/4 teaspoon salt, pepper to taste, and the remaining 1 teaspoon fresh oregano. Serve immediately.