Preheat the oven to 425 degrees F. Place the lamb racks in a roasting pan; season with salt and pepper. Roast the lamb 22 to 25 minutes for rare, 25 to 28 minutes for medium rare, and 30 minutes for medium. When done, set on a plate, tent with foil, and rest 10 minutes. Place the roasting pan on the stovetop over medium-high. Add the remaining ingredients, bring to a simmer, and simmer until the jam is melted and a fluid sauce forms, about 3 to 4 minutes. Cut the lamb into single chops, arrange on a platter or board with a bowl of the blackberry sauce alongside for dipping.