Mix the ingredients for the Sweet-Tart Carrot/Onion Pickle together, taste for sweet-tart balance, and let marinate 30 minutes to three days in the refrigerator. When ready to serve, drain and mix with the chicken filling.
In a glass jar with a screw top, combine all ingredients for the Sweet-Tart Dipping Sauce with Tomato, shaking to dissolve sugar. Taste for balance. Keep in the refrigerator up to 3 weeks. To serve, set out in 4 individual little bowls, one for each diner.
When ready to serve set out the sauce and chicken. Arrange all the roll-up fillings, lettuce cups, tomatoes, cucumber and lime wedges on a large platter. Everyone spoons a little filling into the cups, adds tomato and cucumber, squeezes lime over the mix, rolls them up and dips into the sauce if desired.