In a dry skillet over medium heat, toast the guajillo and ancho chiles until fragrant, about 2-3 minutes. Remove from heat and soak in hot water for 15 minutes.

In a blender, combine the soaked chiles, cumin, oregano, black pepper, and garlic. Blend until smooth, adding a bit of the soaking water if necessary.

In a Dutch oven, heat some oil over medium-high heat. Brown the beef and lamb chunks on all sides. Remove and set aside.

In the same pot, add chopped onion and sauté until translucent. Add the blended sauce and cook for another 5 minutes.

Return the meat to the pot, add beef broth and water, and bring to a boil. Reduce heat to low, cover, and simmer for 2-3 hours until the meat is tender.

Shred the meat and serve in bowls with the broth. Garnish with cilantro, diced onion, and lime wedges. Serve with corn tortillas on the side.