Remove any damaged outer leaves from the radicchio. Cut each head lengthwise through the core into slices about 1½ inches (4 cm) thick, making sure that each slice has a bit of the core attached to hold it together during cooking. (The end slices, which will not be attached to the core, can be reserved for another use, such as salad.) Put the radicchio slices in a single layer in a shallow dish. Drizzle with 1 tablespoon of the olive oil and ½ teaspoon of the lemon juice. Season with half each of the salt and pepper. Turn the slices over and repeat the drizzling and seasoning on the other side. Let stand at room temperature for at least 30 minutes or up to 4 hours before grilling.
When ready to cook, preheat the oven to 325°F (165°C). Oil a grill pan and warm over medium-high heat. Place the radicchio slices in the grill pan and cook until seared and golden on the first side, 3–4 minutes. Turn the radicchio over and grill for 1–2 minutes longer. Transfer the radicchio to a baking dish and top with the cheese, dividing it evenly. Bake until the cheese has melted, about 4 minutes. Serve hot.