Heat a large, cast-iron skillet over medium-high heat.
Season chicken with salt and pepper, and dredge in flour; shake off excess. Add 2 tablespoons of oil to the pan, 2 turns of the pan and brown half of the chicken until crispy and golden on both sides. Remove to a plate, add more oil as necessary and repeat with remaining chicken. Brown both lemon halves, cut-side-down, to caramelize the flesh; reserve.