Cook pasta in a pot of boiling salted water until just tender but still firm to the bite. Drain, reserving 1/2 cup pasta cooking liquid. Return pasta to pot.
Meanwhile, cook pancetta in a large nonstick skillet over medium heat until crisp. Using a slotted spoon, transfer pancetta to paper towels to drain. Pour off all but 1 teaspoon drippings from skillet. Add asparagus to drippings in skillet; saute' 3 minutes. Add peas, white and pale green parts of green onions, and garlic; saute' until vegetables are just tender, about 2 minutes. Remove from heat.
Add vegetable mixture, 1/4 cup pasta cooking liquid, dark green parts of green onions, 1/2 cup Parmesan, cream, olive oil, lemon juice, lemon peel, half of the parsley and half of the basil to the pasta. Toss, adding more cooking liquid by tablespoonfuls if needed. Season with salt and freshly ground black pepper. Transfer to a large bowl. Sprinkle pancetta, remaining parsley and remaining basil over. Serve, passing additional Parmesan cheese.