Fill a large bowl with warm water. Working with 2 sheets of rice paper at a time (keep others covered with a barely damp cloth to prevent curling), immerse papers in the warm water until slightly softened (about 15 seconds). Remove and spread out on a clean surface or cutting board. Pat dry with a towel to remove excess water. Lay 2 pieces of lettuce over the bottom third of the rice paper, leaving about 1/2-inch clear on edges. Place about 1/3 cup chicken and carrot mixture on the lettuce, top with 4 to 5 pieces cucumber, scallion, several mint leaves and about 1 heaping tablespoon of rice. Roll up the paper halfway into a cylinder. Fold both edges in to tuck while continuing to roll the paper to seal. Place the rolls on a plate covered with a damp towel so they stay moist as you prepare the remaining rolls. Cut rolls in half and wrap in plastic wrap or place in an air-tight container.