Heat the vegetable oil in a large skillet over medium-high heat. Add the lamb, and cook until browned on all sides, about 5 minutes. Season with saffron, salt and pepper to taste; stir in all but 1/4 cup of the onion, and pour in the water. Bring to a boil, then cover, reduced heat to medium-low, and simmer until the lamb is tender, about 15 minutes.
Uncover the skillet, stir in the butter, and allow the sauce reduce 5 to 10 minutes to desired consistency. Season to taste with salt and pepper, then pour into a serving dish. Sprinkle with the remaining chopped onions and parsley. Garnish with lemon wedges to serve.