Mix minced shallots, chopped mint, chopped rosemary, minced garlic, sugar, and 1 tablespoon salt in small bowl. Press 1 rounded teaspoon shallot-herb mixture onto eye of each lamb chop. Turn chops over onto large rimmed baking sheet.
Press remaining shallot- herb mixture onto eye of each chop. Cover lamb chops with sheet of plastic wrap and refrigerate overnight.
Whisk olive oil, lemon juice, and lemon peel in small bowl until slightly thickened and well blended. Season lightly with salt and generously with freshly ground black pepper. Spoon oil mixture lightly over chops. Turn chops over and spoon remaining oil mixture over. Let stand at room temperature 1 hour.
Prepare barbecue (medium-high heat). Grill lamb chops to desired doneness, about 3-4 minutes per side for medium-rare. Transfer lamb chops to platter. Garnish with fresh oregano sprigs and serve.