Set the Instant Pot to sauté mode and add the lamb pieces. Cook for 5 minutes, stirring occasionally, until the meat is lightly browned on the outside.
Add the diced onion and minced garlic to the pot. Stir and cook for 3 minutes until the onion starts to soften.
Stir in the chopped chipotle peppers, cumin, smoked paprika, salt, and black pepper. Cook for 1 minute to toast the spices.
Add the diced tomatoes, black beans, and beef broth. Stir everything together, scraping the bottom of the pot to loosen any browned bits.
Secure the lid, set the valve to sealing, and cook on manual high pressure for 35 minutes. Allow a natural pressure release for 15 minutes, then quick release any remaining pressure.
Open the lid and stir the stew. Taste and adjust salt if needed. Ladle into bowls and top with chopped cilantro. Serve with lime wedges on the side.