Light a charcoal grill or preheat a gas or stovetop grill until very hot.
For the sauce, whisk together the lemon juice, olive oil, oregano, red pepper flakes, 1 tablespoon salt, and 1 teaspoon black pepper. Set aside.
When the grill is ready, sprinkle the fish with salt and pepper and cook over medium-high heat for 2 minutes on one side, then turn and cook for 1 to 2 minutes on the other side until almost cooked through. Remove to a flat dish, prick holes in the fish with the tines of a fork, and pour the lemon sauce over the fish while it¿s still hot. Sprinkle liberally with salt and pepper, cover with aluminum foil, and allow to rest for 5 minutes.
When ready to serve, place the swordfish on dinner plates or a serving platter, pile the arugula on top, drizzle with the sauce from the fish, and sprinkle with the grated lemon zest. Serve warm.