Prep the lamb. Pat the racks of lamb dry and trim away any excess fat. Cut them into thick chops (about 1 inch thick or so) and set them aside.
Marinate the lamb. In a small bowl, combine the olive oil, garlic, lemon zest, lemon juice, salt, sugar, and pepper together. Coat the chops evenly with the marinade and transfer to a ziplock bag or into a baking dish covered with plastic wrap. Let them marinade in the fridge for 2-4 hours.
Make the mint-pistachio sauce. Place the pistachios on a small baking sheet and toast them in a 350 F degree oven for 5-7 minutes, until golden. Let them cool and then roughly chop them. In a small food processor, combine the garlic, olive oil, lemon zest, mint, sherry vinegar, and parmesan and pulse until finely chopped. Transfer the contents to a small bowl and stir in the pistachios and season to taste with salt and pepper.
Prep & preheat the grill. Remove the lamb from the fridge 30 minutes before you plan to cook. Preheat an outdoor grill to medium heat. If using charcoal, spread the lit charcoal briquettes in an even layer. The grill should sit at 450-500 F. Clean the grates of any debris.
Grill the lamb chops. Remove the chops from the marinade and shake off any excess. Grill the lamb chops over direct heat for 3-4 minutes per side, or until the internal temperature reaches 130-135 F. Remove the lamb from the grill and transfer to a serving platter. Loosely tent them with foil and let them rest for 10 minutes. Serve drizzled with the mint-pistachio sauce.