For sauce: In a small saucepan, heat sugar over medium-high heat until sugar begins to melt, shaking saucepan occasionally to heat sugar evenly. Reduce heat to low and cook until sugar is melted and light brown (about 3 minutes more). Stir as necessary after sugar begins to melt. Carefully add water (it will splatter), stirring until sugar is dissolved. Remove from heat. Stir together chicken broth, fish sauce, and cornstarch; stir into sugar mixture. Set aside.
Add the 2 tablespoons cooking oil to a wok or a 12-inch skillet. Preheat over medium-high heat (add more oil if necessary during cooking). Stir-fry lemon grass or lemon zest and garlic in hot oil for 15 seconds. Add the onion and carrot; stir-fry for 2 minutes. Add broccoli; stir-fry for 2 minutes. Add sweet pepper and red chili pepper; stir-fry for 2 minutes more or until vegetables are crisp-tender. Remove vegetables from wok.
Add chicken to wok; stir-fry about 4 minutes or until no longer pink. Push chicken from center of wok. Stir sauce; add to center of wok. Cook and stir until thickened and bubbly. Return cooked vegetables to wok; cook and stir about 1 minute or until heated through. Serve immediately over noodles. Sprinkle with cilantro, if desired.