Prepare the Keg for indirect grilling at 300°F, fill the diffuser with water and add lemons.
Cut chicken in half and rub in paprika. Place chicken in foil tray. Slice onions and place in top of the chicken. Pour over marinade. Place onto the keg grill and close lid. Cook for approximately 2 1/2 - 3 hours. Once the internal temperature of the meat has reached 170°F, remove from the Keg and wrap in foil to let rest. At this point, open the vents of the Keg to increase the cooking temperature to around 450°F.
Blanch carrots and green beans until tender-crisp. Drain and rinse under cold water 10 seconds to refresh. Melt the butter mix in a saucepan, and add the rest of the sauce ingredients. Lay the carrots and beans on a grill topper, and brush with half the butter mixture.
Grill the vegetables over direct high heat on the Keg with the lid open until lightly browned for 3-5 minutes, turning occasionally. Transfer the vegetables to a platter and baste with the remaining butter mixture. Serve hot.