Brush plantain slices and lime halves evenly with 1 tablespoon coconut oil. Place plantains and lime halves, flesh-side down, on a greased grill rack. Grill, covered with grill lid, over medium-high heat (350° to 400°) about 4 minutes or until golden brown; set aside.
Sprinkle swordfish with salt and pepper; brush fillets with remaining 2 tablespoons coconut oil. Place fish on a greased grill rack. Grill, covered, over medium-high heat 1 to 2 minutes on each side or until fish flakes with a fork.
Arrange greens on 2 serving plates. Top evenly with fish, plantains, and grilled lime; drizzle with Tomato-Molasses Dressing.