Mix lime juice, olive oil, cumin, salt, pepper and garlic together. Pour over chicken in a ziploc freezer bag. Force out the excess air and message to coat chicken pieces. Refrigerate for at least 3 hours, preferably overnight.
Discard marinade. Pat chicken dry with a paper towel. Season the chicken with additional salt, pepper and a little extra cumin.
Heat up the burners on a gas grill or light charcoal briquettes to preheat the grilling surface. Grill the chicken over medium heat using an indirect heating method to avoid flare-ups. Cook for approximately 30 minutes, turning occasionally until chicken begins to brown.
For the glaze, mix guava jelly, apple juice, lemon juice and brown sugar in a 1-quart saucepan and bring to a boil. Reduce heat to low and simmer, uncovered, stirring frequently until glaze thickens and reduces somewhat, about 5 to 10 minutes; remove from heat.
Brush chicken with glaze mixture frequently during the last 15 minutes of cooking. Once glazed, keep a close eye on the chicken because sugar burns easily and tastes terrible.