Preheat the oven to 400°. In a roasting pan, toss the potatoes, 1/4 cup olive oil, the scallions, rosemary, and peel and juice of 2 lemons; season liberally with salt. Roast until golden and tender, about 40 minutes.
Meanwhile, in a large nonstick skillet, heat 1 tablespoon olive oil with 2 tablespoons butter over medium-high heat. Place the flour in a shallow bowl; season with salt. Dredge 2 chicken breasts in the flour, shaking off any excess. Fry until just cooked through, about 3 minutes on each side. Transfer to a paper-towel-lined plate and keep warm. Add the remaining 1 tablespoon olive oil and 2 more tablespoons butter to the skillet and cook the remaining 2 chicken breasts as above. Transfer to the plate.
Whisk the remaining 1 tablespoon butter and peel and juice of 1 lemon into the pan juices and cook until just browned, about 5 minutes. Pour the lemon-butter sauce over the chicken; serve with the potatoes.