Vietnamese Roast Chicken Veggie Rolls

fresh lime juice , divided

fish sauce

sugar

lime zest

Asian chili sauce

rotisserie chicken , meat removed and shredded, skin and carcass discarded

rice vermicelli noodles

large carrot

English cucumber , seeded

8.5-in.-round rice paper wrappers

green onions , cut into long strips

packed cilantro

packed mint

Thai basil leaves

Boston lettuce leaves