Preheat oven to 350 degrees F.
Heat olive oil in a large Dutch oven and sear lamb chops until golden brown on both sides. Remove to a plate. Add onions, carrots, and celery to the pan and cook until the vegetables are golden brown. Add red wine and port and cook until almost reduced.
Add the chops back to the pot, add the stock, bay leaf, thyme, and bring the stock to a boil. Cover the pot, place the pot in the oven, and cook for about 2 hours or until fork tender.
Remove the lamb to a plate, strain into a clean small pot, and cook until reduced to a sauce consistency. Swirl in butter and season with salt and pepper, to taste.
Place a square of Potato-Artichoke Gratin on a large plate, top with a lamb chop and ladle some of the sauce over and around. Garnish with a sprig of fresh thyme and chopped parsley.
Place the artichokes, onion, lemon, wine and water to cover in a medium saucepan, cover with a clean dish cloth and simmer over medium-high heat until the artichokes are tender, about 20 to 30 minutes.
Drain the artichokes and when cool enough to handle, cut off the top half, trim leaves, remove choke, and remove heart. Slice heart into thin slices.
Preheat oven to 375 degrees F.
Butter a 8 x 8-inch baking dish and place a layer of potatoes on the bottom, place 1/4 of the artichoke hearts over the potatoes, season with salt and pepper, drizzle with 1/4 cup of the cream and some of the thyme. Repeat to make 5 layers ending with a layer of potatoes. Combine the cheese and bread crumbs and sprinkle over the top.
Place on a baking sheet and bake for 35 to 40 minutes or until the potatoes are cooked through and the top is golden brown and bubbly. Let rest 10 minutes before cutting.