Add garlic, ginger, and lemongrass to a food processor and pulse until finely chopped. Set aside.
Add oil to a large pot or Dutch oven over medium-high heat. Add garlic mixture, green onions, and water chestnuts and saute until soft and fragrant, about 3-5 minutes.
Add chicken broth and chicken to the pot. Reduce heat to medium and let come to a simmer, about 7 minutes.
Add dumplings and cook according to package directions. If using fresh dumplings, they only need 2-3 minutes to cook through but may take longer if using frozen.
Add the vegetables and cook for 2-3 minutes longer or until everything is steaming and the vegetables have softened. Stir in the soy sauce, lime juice, and sesame oil, then ladle into bowls and garnish with cilantro, sliced green onions, sesame seeds, and serve with additional soy sauce
Ladle into bowls and garnish with cilantro, sliced green onions, sesame seeds, and serve with additional soy sauce.