Preheat oven to 425°. In a 13"by-9" baking dish, toss potatoes, lemon, 2 tablespoons oil, ¼ teaspoon salt, and a few grinds of pepper. Roast until potatoes just start to turn golden, 14 to 16 minutes.
Pat chicken dry with paper towels; season all over with 1 ½ teaspoons salt and ¼ teaspoon pepper. Nestle chicken skin side up between potatoes. Sprinkle chicken with paprika and drizzle with remaining 1 tablespoon oil.
Roast chicken until skin is golden brown and an instant-read thermometer inserted into thickest part (without touching bone) registers 165° and potatoes are crisp and golden brown, about 35 minutes.
Using tongs or a slotted spoon, transfer chicken and potatoes to a platter. Carefully stir garlic into hot pan drippings (there should be about ½ cup drippings). Add parsley, olives, almonds, vinegar, and 1 teaspoon salt; stir to combine.
Spoon sauce over chicken and potatoes. Crumble feta over top.
