IN A LARGE HEAVY-BOTTOMED SOUP POT, heat the oil over medium heat. Add the onion, celery, garlic, sage, a good pinch of salt, and a few cracks of pepper. Stir to coat the vegetables and cook until the onion and celery become translucent, about 5 minutes.
Add the beans and another good pinch of salt, then add the lamb shank and stock. Increase heat to medium-high and bring the stock to a boil. Reduce to a simmer and cook until the beans are al dente, 45 to 60 minutes.
Add the carrots and continue cooking until the beans and carrots are tender, about another 15 minutes.
Remove the shank from the soup and transfer in to a cutting board to cool slightly. Shred the meat from the bone, add it back to the soup, and discard the bone. Sprinkle the stew with lemon juice and season as needed with more salt/pepper.