Whisk in wine, then broth, until smooth. Increase heat to medium-high, bring to simmer, and cook until sauce is slightly thickened and measures 21/2 cups, about 15 minutes; transfer to liquid measuring cup and cover to keep warm.
Meanwhile, bring 4 quarts water to boil in large pot. Add pasta and 1 tablespoon salt and cook, stirring often, until al dente. Reserve 1/2 cup cooking water, then drain pasta and return it to pot. Add 2 cups sauce, arugula, Parmesan and lemon juice, and toss until arugula is slightly wilted. Add reserved cooking water as needed to adjust consistency and season with salt and pepper to taste.
Slice chicken thinly on bias. Portion pasta into individual bowls, lay chicken over top and drizzle remaining 1/2 cup sauce over chicken. Serve with extra Parmesan.