Place the ancho chiles in a bowl and cover them with hot water. Let them soak for 20 minutes until soft, then remove the stems and seeds.
Heat the vegetable oil in a Dutch oven over medium-high heat. Add the lamb pieces and brown them on all sides, working in batches if needed. Remove the lamb and set it aside.
Add the chopped onion to the same pot and cook until it softens. Stir in the minced garlic, cumin, and oregano, and cook for one more minute.
Drain the soaked chiles and blend them with 1 cup of the chicken broth until smooth. Pour this mixture into the pot with the onions.
Return the browned lamb to the pot and add the remaining chicken broth. Season with salt and black pepper. Bring the stew to a simmer, then cover and cook on low heat for 1 hour and 30 minutes.
Stir in the drained hominy and continue simmering uncovered for 20 more minutes until the lamb is fork-tender and the broth has thickened slightly.
Ladle the stew into bowls and top each serving with chopped cilantro. Serve with lime wedges on the side.