Sprinkle chicken with pepper and 1/2 teaspoon of the salt; dredge in flour, shaking off excess.
Heat oil in a large skillet over medium-high. Add chicken and lemon halves, cut side down. Cook until chicken is lightly browned and cooked through, about 2 minutes per side. Transfer chicken and lemons to a serving platter; tent with aluminum foil to keep warm.
While chicken is cooking, prepare broccoli according to package directions; set aside.
Add wine to skillet over medium-high; bring to a boil, scraping bottom of skillet to loosen browned bits. Cook, until almost completely reduced, about 2 minutes. Add chicken broth; cook until slightly reduced, about 3 minutes. Remove from heat. Add capers, lemon juice, butter, and remaining 1/8 teaspoon salt, and stir until butter is melted.
Place broccoli on platter with chicken; drizzle with pan sauce, and sprinkle with parsley.