In a large bowl, mix together the shredded chicken, black beans, cream of chicken soup, green enchilada sauce, chopped green chiles, fresh cilantro, and lime juice. This is your hearty, flavorful enchilada filling.
Cut three 30x6-inch strips of heavy-duty foil and crisscross them inside the round 4- or 5-quart slow cooker to create handles. Coat the foil strips with nonstick cooking spray.
Start layering: Spread 1/4 cup of the chicken mixture on the bottom of the slow cooker. Top with 3 tortillas (overlapping and tearing if needed to fit), 1/3 of the chicken filling, and 1/3 of the cheese. Repeat this process twice more, ending with cheese as the top layer.
Cover and cook on low for 4 hours, or until the internal temperature reaches 165°F. To prevent scorching, rotate the slow cooker insert halfway through the cooking time if possible.
Once done, turn off the slow cooker and let the pie rest for 15 minutes uncovered. Use the foil handles to carefully lift the enchilada pie out of the slow cooker, then transfer it to a serving platter.
Slice into wedges and serve with optional garnishes like fresh cilantro, lime wedges, salsa, or sour cream.