Prepare the marinade by adding the vinegar, lemon juice, paprika, dried herbs, garlic powder, ½ tsp each of salt and pepper to the melted butter in a small bowl.
Place the chicken in a shallow dish or large freezer baggie. Pour the marinade into the dish, or baggie. Cover the dish with plastic wrap, or press the air out of the baggie and close. Place in the fridge for 3 to 24 hours.
Fire up your grill to 2-zone heat (half direct heat and the other half no heat). Optimal internal gill temperature is between 325° and 400°F.
Remove the chicken from the marinade and place on the no-heat side of the grill. Save the marinade.
After about 10 minutes on the grill, sprinkle the chicken with a little salt and pepper. Use a brush to apply some of the reserved marinade to the chicken. Use tongs or a spatula to flip the chicken, and add a little more salt and pepper and then a layer of marinade.
Baste and flip the chicken about every 10 to 15 minutes, basting each time, for approximately 45 minutes, or until the internal temperature of the chicken reaches 145°F.
Transfer the chicken to the direct-heat side of you grill. Place the lemons on the grill, cut side down, over direct heat.
Discard any of the marinade and get a new brush, or clean the one you were using. Brush the chicken with a little more melted butter. Cook until the exterior is crispy and an internal temperature of 160° to 165°F has been reached.
Remove from grill and serve with grilled lemons.