Preheat your oven to 400 degrees Farenheit. You’ll be using bottom rack of your oven.
Prepare your lamb shoulder by trimming away any excess fat. Place your lamb in the center of a large roasting pan, one which is just large enough to hold the lamb and all of the potatoes.
Pour 1/4 cup freshly squeezed lemon juice over your lamb shoulder and then sprinkle your lamb evenly with 1 tablespoon salt, 1 teaspoon ground black pepper, and 1 tablespoon Greek oregano.
Peel your potatoes and cut them into thick wedges (for small to medium sized potatoes, cut them in quarters, and for larger potatoes, cut them into 6 wedges).
Place your potatoes into the roasting pan, surrounding the lamb. Pour 1/4 cup freshly squeezed lemon juice over your potatoes. Evenly sprinkle your potatoes with 3/4 teaspoon salt, and 1 tablespoon oregano.
Pour the olive oil and vegetable oil over your lamb and potatoes.
Place your roasting pan on the bottom rack of your oven, uncovered. Cook for 1 hour and 30 minutes. Remove roasting pan from oven and sprinkle 1 teaspoon of paprika over the potatoes. Turn your lamb shoulder over. Cover the lamb loosely with aluminum foil. Leave the potatoes uncovered.
Return to oven and cook for an additional 45 minutes. Check your potatoes for doneness. They should be soft and golden yellow.
Allow your lamb to rest for 5 – 10 minutes before carving, to allow juices to settle.
Enjoy!