1. Peel and segment grapefruit with a sharp knife on a cutting board; reserve juice in a bowl. Toss grapefruit segments and juices with arugula and avocado; divide salad among 4 serving plates. In a small bowl, whisk together lemon juice, oil, and 1/4 teaspoon each salt and pepper.
2. Sprinkle remaining salt and pepper over both sides of salmon. Coat a large nonstick skillet with cooking spray; heat over medium-high heat. Add fish (skin-side down) to skillet, and cook until skin is golden and fish releases easily from pan (about 4 minutes). Using a spatula, gently flip fish and cook about 3 minutes more. Break each fillet into 4 pieces; top salads with 3 pieces fish. Drizzle salads with reserved dressing; sprinkle with walnuts.