Rub the lamb with olive oil, then sprinkle with salt and pepper. Preheat a 14-inch cast-iron pan over medium-high heat. Add the seasoned lamb and sear for 5 minutes. Transfer the pan to the oven and roast until browned, about 30 minutes.
Meanwhile, place a large Dutch oven over medium-high heat and add 2 tablespoons olive oil. Once heated, add the leeks and onions and cook until they begin to become tender, about 3 minutes. Set aside.
After 30 minutes, remove one of the lamb shoulders from the oven and set aside. Add half of the turnips to the pan and return to the oven. Allow to continue roasting until everything is cooked through, about another 30 minutes.
Add the other lamb shoulder to a stovetop pressure cooker along with the cooked leeks, onions, beer and remaining turnips. Secure the pressure cooker lid and follow the manufacturer's instructions to bring to high pressure over medium heat. Pressure cook for 20 minutes. Follow the manufacturer's instructions to carefully quick-release the steam and unlock the lid. Add everything in the pressure cooker to a large pan or shallow dish and stir, breaking up the lamb. Add to a platter. Add the roasted lamb and turnips to the same platter and serve.