Heat the canola oil over medium-high heat in a medium, heavy pot or Dutch oven. Place the lamb shanks in the pot and sear for two minutes on each side. Remove the lamb from the pot and set aside. Add the carrot, celery, and onion to the pot and saute for two minutes, stirring constantly. Add the lemon juice, soy sauce, Worcestershire sauce, sage, thyme, rosemary, mustard, onion powder, salt, pepper, and chili flakes. Stir to incorporate.
Return the lamb shanks to the pot and add the water. Turn the heat down to medium-low, cover, and leave to braise for two hours, or until the meat is very tender. Turn off the heat, transfer the lamb shanks to a plate, and allow them to sit for 15 minutes. Then, using two forks, pull all the meat from the bones and shred it into medium chunks. Discard the bones and stir the lamb meat back into the gravy in the pot. Cover and keep warm.
Place the potatoes in a medium saucepan and cover with water. Bring to a boil and cook until fork-tender, about ten minutes, then drain. Melt the butter in a large frying pan over medium-high heat. Add the potatoes and fry until crispy all over. Add them to the Braised Lamb.
In a medium frying pan, heat the canola oil over medium-high heat. Crack the eggs into the pan and turn the heat down to medium. Cook the eggs sunny side up for about five minutes.
Serve the Lamb Shank Hash on a large platter with sunny-side-up eggs on top.