Preheat the oven to 325°F (160°C). Pat the Bone-In Lamb Shoulder dry and season generously on all sides with Salt and Black Pepper.
Heat a large, heavy Dutch oven or ovenproof pot over medium-high heat and add a drizzle of Olive Oil and a knob of Unsalted Butter. When the fat is hot, brown the lamb on all sides until a deep crust forms, about 4–6 minutes per side. Transfer the lamb to a plate and set aside.
Reduce the heat to medium and add the chopped Spring Onions to the pot; sauté until softened and fragrant, about 3–4 minutes. Pour in a cup or two of Water to deglaze the pan, scraping up browned bits from the bottom with a wooden spoon.
Return the lamb to the pot, nestle it into the liquid, cover tightly, and transfer the pot to the oven. Braise until the meat is very tender and pulling away from the bone, about 2–2½ hours (check after 1½ hours to top up liquid if needed).
About 20 minutes before the lamb is done, add the Peas and torn Lettuce leaves around the meat so they steam gently and wilt without losing color; recover and finish cooking.
When the lamb is tender, remove the pot from the oven. Stir in Lemon Juice to taste and sprinkle in chopped Dill and torn Mint Leaves. Adjust seasoning with additional salt and pepper if needed, spoon the glossy pan juices over the meat, and serve warm.
