In a large frying pan over high heat, cook onions in 3 tablespoons olive oil with sugar and 2 teaspoons salt, stirring and turning often, until onions begin to release their juices and turn golden, 10 to 13 minutes. Reduce heat to medium and cook, stirring occasionally, until onions turn a caramel color and become quite sweet, 35 to 40 minutes more. If onions begin to stick to the pan or char during cooking, reduce heat.
Meanwhile, in a small frying pan (not nonstick) over medium-low heat, toast walnuts, stirring frequently, until fragrant and golden, about 10 minutes. Remove from heat and cool slightly. Pour walnuts into a zip-lock plastic bag and lightly crush with a rolling pin. Set aside.
When onions are nearly done, cook pasta in boiling salted water until tender to the bite, 9 to 12 minutes or according to package instructions. Drain pasta, reserving about 1/2 cup cooking water.
Toss caramelized onions with pasta, walnuts, ricotta salata, parsley, reserved cooking water, lemon juice, pepper, and remaining 2 tablespoons olive oil. Season to taste with salt. Serve hot.
Note: Nutritional analysis is per serving.