In a food processor combine the parsley, mint, oregano, anchovy, and garlic. Pulse to finely chop. Add 1/3 cup oil and process to form a chunky salsa. Transfer to a bowl and stir in the capers, salt, and black pepper. Set aside while you cook the lemons and swordfish.
Prepare the grill for direct cooking over medium heat (350° to 450°F). Preheat the griddle direct medium heat for 10 minutes.
In a bowl combine the lemon slices and 1 teaspoon oil and stir to coat. Arrange the lemons on the griddle and cook, with the lid closed, until the lemons are sizzling and charred on both sides, turning once or twice, 4 to 5 minutes. Transfer to a cutting board and finely dice. Add to the salsa with any collected juices.
Brush the swordfish with oil and season with salt and black pepper.
Cook the fish on the griddle over direct medium heat, with the lid closed, until just opaque in the center but still juicy, 8 to 10 minutes. Transfer to serving plates. Serve with the salsa verde.