Heat the vegetable oil in a large Dutch oven over medium heat. Add the lamb cubes and cook until browned on all sides, about 5-7 minutes. Remove the lamb and set it aside.
Add the diced onion to the same pot and cook until softened, about 3 minutes. Stir in the minced garlic and grated ginger and cook for 1 minute more.
Stir the red curry paste into the onion mixture until it coats everything evenly. Return the browned lamb to the pot.
Pour in the coconut milk and beef broth. Add the salt and black pepper, then bring the mixture to a gentle simmer.
Add the sweet potato cubes to the pot. Cover and simmer for 45-50 minutes, stirring occasionally, until the lamb is tender and the sweet potatoes are soft.
Taste and adjust seasoning if needed. Ladle the stew into bowls and top with chopped cilantro. Serve with lime wedges on the side.