Pat chicken dry with paper towels. Grind fennel seeds in a spice mill or with a mortar and pestle. Combine fennel, hot paprika, salt, smoked paprika, black pepper, garlic, and olive oil in a medium bowl; rub spice mixture all over chicken. Rub any leftover spice mixture onto lemon quarters.
Place chicken, breast side up, on a rimmed baking sheet or in a 12-inch ovenproof skillet; scatter lemons around chicken. Roast at 325°F for 1 hour or until chicken is tender, lemons are soft and jammy, and a meat thermometer inserted into thickest portion of breast registers 160°F, basting chicken with drippings every 30 minutes. Remove from oven; rest 15 minutes. Squeeze lemons over chicken, or serve lemons with warm chicken.