Prepare the Chiles:
In a dry skillet over medium heat, toast the guajillo, ancho, and pasilla chiles until fragrant, about 2 minutes.
Transfer chiles to a bowl and cover with hot water. Let them soak for 15 minutes until softened.
Make the Adobo Sauce:
Drain the soaked chiles and place them in a blender.
Add garlic, cumin seeds, oregano, cloves, cinnamon, vinegar, and water.
Blend until smooth. Strain the sauce through a fine mesh sieve to remove any solids.
Marinate the Lamb:
In a large bowl, combine the lamb chunks with the adobo sauce, ensuring all pieces are well coated.
Cover and refrigerate for at least 2 hours, preferably overnight.
Cook the Birria:
In a large pot or Dutch oven, place the marinated lamb along with sliced onion, minced garlic, bay leaves, salt, pepper, and water.
Bring to a boil, then reduce heat to low. Cover and simmer for 3.5 to 4 hours, until the meat is tender and easily shreds with a fork.
Serve:
Remove the lamb from the pot and shred the meat.
Strain the remaining broth to serve as consomé.
Serve the birria in warm corn tortillas, topped with chopped onion, cilantro, and a squeeze of lime. Accompany with a cup of the rich consomé for dipping.