For sauce, in a small bowl stir together broth, lemon juice, cornstarch, and the 1 tablespoon soy sauce; set aside.
Pour 1 tablespoon of the oil into a large skillet; heat skillet over medium-high heat. Add stir-fry vegetables; cook and stir for 5 to 7 minutes or until crisp-tender. Remove from skillet.
Add the remaining 1 tablespoon oil to skillet; add half of the chicken. Cook and stir for 2 to 3 minutes or until chicken is no longer pink. Remove from skillet. Repeat with the remaining chicken (add more oil if necessary). Return all of the chicken to skillet; push from center of skillet.
Stir sauce; add to center of skillet. Cook and stir until thickened and bubbly. Return vegetables to skillet; stir all ingredients together to coat with sauce. Cook and stir for 1 to 2 minutes more or until heated through. Serve with hot cooked rice. If desired, pass additional soy sauce.