In a small saucepan over medium heat, combine sugar, cranberries, orange juice, rind, Dijon mustard and allspice. Cook until mixture boils and cranberries pop (about 10 to 12 minutes). Set aside.
In a preheated broiler, 4” from heat, broil lamb chops on one side for 6 minutes. Turn chops and broil 4 minutes longer. Spoon one generous teaspoonful of sauce over each chop. Broil for 1 minute longer. Serve extra sauce on the side.