Mix together the fennel, tomatoes, green olives, garlic, lemon zest and two-thirds of the lemon juice in a bowl until well combined. Gradually whisk in enough oil to loosen the mixture.
Transfer the fennel and tomato mixture to a pan and slowly bring to the boil, then remove the pan from the heat and set aside until completely cool. Season the sole, inside and out, with salt and freshly ground black pepper.
When the filling mixture has cooled, spoon it into the fish cavities. Drizzle the remaining lemon juice over the stuffed lemon sole.
Transfer the lemon sole to a roasting tray and bake for 8-10 minutes, or until the lemon sole are completely cooked through. (NB: the lemon sole are cooked through when the juices run clear when the fish is pierced in the fleshy part behind the head with a skewer.)
To serve, place each stuffed lemon sole onto a serving plate. Sprinkle over the chopped parsley. Spoon the lightly dressed green salad alongside.