In a small saucepan, combine the first seven ingredients. Bring to a boil. Reduce heat; simmer, uncovered, for 5 minutes. Remove from the heat; stir in lime juice and zest; set aside.
In a small bowl, combine the chicken, dried cranberries, carrot, green onions, mint and basil. Place about 3 tablespoons chicken mixture on each lettuce leaf. Top with 1 tablespoon cranberry sauce mixture and 2 teaspoons peanuts. Fold lettuce over filling. Serve with remaining sauce.