1. To prepare rolls, add hot water to a large, shallow dish to a depth of 1 inch. Place 1 rice paper sheet in dish, and let stand for 30 seconds or just until soft. Place sheet on a flat surface. Arrange 1/4 cup lettuce over half of sheet, leaving a 1/2-inch border. Top with 1/4 cup bean threads, 2 tablespoons sprouts, 2 tablespoons carrot, 1 tablespoon mint, 1 tablespoon cilantro leaves, and 1 1/2 teaspoons green onions. Folding sides of sheet over filling and starting with filled side, roll up jelly-roll fashion. Gently press seam to seal. Place roll, seam side down, on a serving platter (cover to keep from drying). Repeat procedure with remaining roll ingredients.
2. To prepare sauce, combine sugar and the remaining ingredients in a small bowl, stirring with a whisk until sugar dissolves. Serve sauce with rolls.