Start by brining the chicken. This should be done at least 6 hours before grilling.
Place cut up chicken in a large stock pot covered with water at least 3 inches over top of chicken.
Add salt, and lemon juice along with zest of the lemon.
Store in refrigerator 6 hours or overnight.
Remove chicken from water and discard water.
Pre-heat grill to high.
With paper towels, dry off chicken and rub chicken with olive oil.
Place chicken pieces on grill and "char" chicken, turning as to not burn chicken (about 10 minutes) Lower temp to medium and cook chicken till juices run clear when pierced with fork (about 45 minutes)
Remove from grill and allow to cool to the touch.With your hands, remove all skin and set aside. Pull all chicken from bones and place in large bowl.
Take charred skin and dice finely and add to chicken (optional, but adds great flavor).
Add cilantro, juice of two limes, garlic, cumin to chicken and mix to combine.
Set aside and prepare lettuce slaw by adding lettuce, carrots, diced green onions,and juice of 1 lime.