Remove and reserve the greens from the radishes. Cut each radish into 8 wedges.
Cook the pasta according to package directions in a large saucepan or stockpot; reserve 1 cup of the cooking water.
Meanwhile, cook the pancetta in a large skillet over medium until crisp; remove with a slotted spoon, reserving the drippings in the skillet. Add the radishes and cook until tender, about 7 minutes. Add the garlic and reserved radish greens; cook until the greens are wilted.
Toss together the radish mixture, pasta, lemon juice, salt, and pepper. Add the reserved pasta cooking water as needed. Top with the pancetta and Parmesan.