Preheat an outdoor grill to medium-high, or position a rack in the center of the oven and preheat to 400°.
Tear off 4 pieces of heavy-duty foil (or 1 piece to fit a baking sheet if you’re using the oven) and brush with about 1 tablespoon EVOO total. Using the scallions and lemon slices, arrange 4 beds for the sea bass fillets on the pieces of foil. Season the fillets all over with salt and pepper and set 1 on top of each bed.
In a medium bowl, combine the tomatoes, anchovies, olives, capers, parsley, garlic, crushed red pepper and the remaining 2 tablespoons EVOO. Pile one-quarter of the sauce over each fish fillet. Top with another sheet of foil and pinch all the edges to seal, making a pouch.
Place the fish pouches on the grill (or place the baking sheet in the oven) and cook for 17 minutes. Using a large spatula, lift the fish off the lemon slices and transfer to plates. Spoon the juices over the fish and serve with crusty bread and extra EVOO for dipping.