Combine 1 tablespoon soy sauce, cornstarch, and ginger in medium bowl. Add ground turkey, cilantro, scallions, and water chestnuts, and mix well.
Place wonton wrappers on work surface. Spoon a rounded teaspoon of turkey mixture onto center of each wrapper. Place some filling in center of a wonton wrapper and brush the edges of the wrapper with water. Fold the wonton wrapper over the filling and pinch the edges together by making small pleats.
Spray large heatproof plate with cooking spray. Place 12 dumplings on plate. Place round cake rack in large skillet and pour in water to come just to bottom of rack. Cover and bring to a boil over medium heat. Place plate of dumplings on rack, cover, and steam until filling is firm and cooked through, about 5 minutes. Remove and keep warm. Repeat with remaining dumplings.
Meanwhile, combine remaining 2 tablespoons soy sauce, lime juice, and sugar in small skillet over low heat and cook just until sugar has melted, about 1 minute.