Boil large pot of water with tablespoon salt. Season chicken with its salt and pepper; lightly flour and shake off excess.
Heat oil in large skillet over medium; cook cutlets 4 to 5 minutes per side until golden and at least 165°F. Rest on board.
Add wine and broth; scrape browned bits. Simmer 3 minutes; add lemon juice and capers and cook 1 minute.
Meanwhile, cook pasta according to package. Reserve 1/2 cup water; drain. Remove sauce from heat; swirl in cold butter.
Toss pasta with sauce, adding water by tablespoon if needed. Slice chicken; serve over noodles.