Preheat grill to high. Stir together the lime juice, salt, and ¼ cup (4 tablespoons) of the oil in a small bowl. Add the onion and let stand at least 10 minutes. Add the haricots verts, bell peppers, and cilantro; toss to combine.
Meanwhile, sprinkle the steak with the black pepper and drizzle with the remaining 1 tablespoon of oil. Grill until an instant-read thermometer inserted in the center of each piece registers 130°F, 5 to 7 minutes per side for medium-rare. Let stand 5 minutes; cut against the grain into thin slices. Serve with the slaw.
