Combine fish sauce, soy sauce, and sugar in a small bowl and set aside.
Heat a large cast-iron skillet or wok over high heat, add oil, and toss in the Thai chilies and garlic. Cook for about 30 seconds.
Turn down the heat to medium-high and add the chicken, breaking up with a wooden spoon and cooking for about 5 minutes, until chicken is almost cooked through.
Pour in the soy mixture and cook for 30 more seconds. Then add in the basil, carrots, and tomatoes and cook for about 30 more seconds, until basil begins to wilt and tomatoes are warmed through. Stir in scallions.
Spoon chicken mixture into individual lettuce leaves.