Layer fennel, onion, and apple slices in a salad bowl and drizzle apple with 1 teaspoon lemon juice. Top salad with red grapefruit sections, toasted walnuts, and basil leaves.
Whisk 2 teaspoons lemon juice with lime juice, grapefruit juice, and olive oil in a small bowl; season to taste with salt and black pepper. Drizzle dressing over salad and serve.