For the ketchup: Place the tomato sauce, onion, vinegar, sugar, tomato paste, salt, and cinnamon stick (or ground cinnamon, if using) in a medium saucepan. Bring the mixture to a simmer and cook, stirring occasionally, until thick, about 1 hour. Remove the onion and cinnamon stick and discard. Cool for 30 minutes and refrigerate until ready to use (can be refrigerated for up to 1 week).
For the lamb chops: Place a grill pan over medium-high heat or preheat a gas or charcoal grill. Season the chops on both sides with salt and pepper. Drizzle with oil and sprinkle the herbes de Provence on both sides. Grill on each side until medium-rare, 2 to 3 minutes. Cool for 5 minutes and serve with the ketchup.
Cook's Note: The lamb chops can also be roasted or broiled in a preheated 475 degrees F oven for 6 to 7 minutes.