Heat 2 tablespoons of olive oil in a dutch over over medium-high heat. Add the lamb shoulder and sear on all sides until golden brown, about 5 minutes per side. Transfer lamp to a plate. Add the 2 remaining tablespoons of olive oil and the chopped onions, and saute until the onions are golden brown, stirring occasionally, about 5 minutes. Add the garlic and saute until softened, about 2 minutes. Add the sugar, 1 teaspoon salt, and thyme, and stir to combine. Return the lamb to the pot and add 4 tablespoons of water. Place a lid on the pot and bring the liquid to a simmer. Transfer the pot into the oven and cook for 5 hours.