In a small bowl, whisk the cornstarch with the water. Next, whisk in the lime juice, fish sauce, brown sugar, Sriracha and soy sauce (tamari). Set aside.
Heat the oil in a 10 inch cast iron or your favorite skillet over medium heat. Add the onions and cook a few minutes, until they become fragrant. Add the garlic and ginger cook another 1 minutes. Add the carrots, cook 2 minutes.
Increase the heat to medium high and add the ground chicken. Mix in the chicken and make sure to chop it into small pieces as it cooks. Once the chicken is white and has almost cooked through, about 4-5 minutes, pour in the sauce and mix well to combine. Cook for 1 minute until the sauce thickens a bit. Mix in the cilantro.
Remove the skillet from the heat. Arrange the lettuce leaves on a large serving plate. Spoon the chicken filling into the lettuce leaves. Top with any of the serving suggestions. Serve immediately.