In a large casserole dish, whisk the lemon juice, extra-virgin olive oil, and salt to blend. Add the chicken pieces and turn to coat. Cover and refrigerate at least 2 hours and up to 1 day, turning the chicken pieces occasionally.
In a large cast iron frying pan or other heavy frying pan, add enough oil to come 1/3-inch up the sides of the pan. Heat the oil over medium heat. Meanwhile, drain the marinade from the chicken. Pat the chicken dry with paper towels. Sprinkle with pepper. Working in 2 batches, dredge the chicken in the flour to coat completely. Shake off the excess flour and then carefully add the chicken to the hot oil. Fry until the chicken is golden brown and just cooked through, turning occasionally, about 25 minutes. Using tongs, transfer the chicken to a paper towel-lined plate to drain the excess oil.
Arrange the fried chicken on a warm platter and serve with the lemon wedges and parsley.