With a large, heavy knife or sturdy kitchen scissors cut down either side of the backbone of 1 chicken. Open out the chicken and press to flatten with your hands. Loosen the skin over the breast and legs. Repeat with the other chicken.
Mix the ricotta, Parmesan, basil, lemon zest and some seasoning. Spoon the stuffing between the skin and flesh of the chickens, spreading it as evenly as possible over the breast and the tops of the legs. Fold the skin back over the stuffing and use your hands to continue to smooth the stuffing over the breast and onto the tops of the legs.
Season the chickens all over, then sprinkle with lemon juice and olive oil and rub over the skin. Push two large metal skewers into each chicken in a cross shape through the legs to keep them flat and make them easier to turn.
Cook, skin-side down, for 20-25 mins over a moderate heat, then turn over and cook for a further 20-25 mins. Check they are cooked by piercing the thickest part of the leg. If the juices run clear the chicken is cooked. If not, continue to cook for a further 10 mins and test again. Transfer chickens to a large board and cut into portions to serve.