Poke surface of chicken all over with a knife or fork. Rub chicken pieces on all sides with cut surfaces of lemons, squeezing to release some of the juice; reserve remaining juice for grilling
Combine salt, garlic, paprika, and pepper in a bowl. Brush chicken with 1/2 of the melted butter; sprinkle with 1/2 of the seasoning mix.
Preheat an outdoor grill for medium heat and lightly oil the grate.
Cook chicken on the preheated grill for 7 to 10 minutes. Flip, squeeze remaining lemon juice over chicken, brush with remaining butter, and sprinkle with the rest of the seasonings. Continue to grill until no longer pink in the centers and juices run clear, 8 to 10 minutes more. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Sprinkle chicken with sugar just before serving. Grill cooked chicken for 2 minutes more. Serve.