NOTE: Look for fish sauce, rice stick noodles, and lemongrass at better supermarkets and at Asian markets.
Whisk first 4 ingredients, 2 teaspoons ginger, and garlic in a small bowl until sugar dissolves. Set dressing aside.
Cook noodles in a large pot of boiling salted water until tender but still firm to the bite, 2-4 minutes. Drain; put in a large bowl.
Meanwhile, heat 2 tablespoons oil in a large skillet. Add chicken; stir 1 minute. Add 1 tablespoon ginger, shallot, and lemongrass. Stir until chicken is cooked through, 3-4 minutes.
Add to noodles. Add half of all herbs and half of dressing; toss to coat.
Line bowls with lettuce leaves. Divide noodle mixture among bowls.
Top with remaining herbs and dressing.