How to Make It
In a small saucepan, combine 1/2 cup of the water with the sugar and bring to a boil over high heat. Boil without stirring until an amber caramel syrup forms, 6 to 8 minutes. Remove from the heat and carefully pour in the remaining 1/2 cup of water. Boil until the caramel is syrupy, about 4 minutes longer. Swirl in the lemon juice. Transfer the caramel sauce to a medium bowl.
In a bowl, mix 2 tablespoons of the fish sauce with the cornstarch and pepper; add the chicken and stir to coat.
In a wok, heat 2 tablespoons of the oil until smoking. Add the lemongrass, onion, garlic and ginger and stir-fry over high heat until the garlic is golden, about 2 minutes. Add the remaining 1 tablespoon of oil. Add the chicken and stir-fry until the chicken turns white, about 3 minutes. Add the carrot, the remaining 2 tablespoons of fish sauce, the cayenne and 3 tablespoons of the caramel sauce and cook over moderate heat, stirring, until the chicken is glazed, about 4 minutes. Stir in the broth, simmer for 30 seconds and serve.