Coat a large plate with 1 teaspoon of the oil; set aside. In a medium bowl, combine the pork, 3 tablespoons water, cilantro, ½ teaspoon pepper, minced scallions, 2 tablespoons of the fish sauce and the 2 teaspoons sugar.
Mix vigorously with a rubber spatula until thoroughly combined, 20 to 30 seconds. The mixture will be soft and sticky. With lightly moistened hands, form into 20 balls and place on the prepared plate. Cover with plastic wrap and refrigerate for 15 minutes.
Meanwhile, in a small bowl, stir together the lime juice, the 3 remaining tablespoons fish sauce, the remaining 2 tablespoons sugar and the chilies until the sugar dissolves. Set aside.
Line another plate with paper towels. In a 12-inch nonstick skillet over medium-high, heat the remaining 2 teaspoons oil until beginning to smoke. Add the meatballs and cook undisturbed until the bottoms are golden brown, 1 to 2 minutes.
Using a spatula, turn each meatball and continue to cook, adjusting the heat as needed and occasionally turning the meatballs, until golden brown all over, 4 to 5 minutes. Transfer to the prepared plate, tent with foil and let rest 5 minutes.
In a small bowl, toss the shredded carrots with 2 tablespoons of the lime juice sauce. Serve the meatballs with the carrots, cilantro sprigs, sliced scallions and lettuce leaves for wrapping. The remaining sauce can be spooned onto the wraps.