Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with olive oil.
In a large bowl, combine the shredded chicken (or ground beef), black beans, corn, diced tomatoes with green chilies, taco seasoning, salt, and pepper. Mix well.
Spread a thin layer of salsa on the bottom of the prepared baking dish.
Place 3 corn tortillas over the salsa, slightly overlapping them.
Layer half of the chicken mixture over the tortillas, followed by 1 cup of cheddar cheese and 1 cup of Monterey Jack cheese.
Repeat the layering process: add 3 more tortillas, the remaining chicken mixture, and another cup of each cheese.
Top with the last 3 tortillas, the remaining salsa, and the remaining cheese.
Cover the dish with aluminum foil and bake for 25 minutes. Remove the foil and bake for an additional 15 minutes, or until the cheese is bubbly and golden.
Let the lasagna cool for 10 minutes before slicing. Garnish with chopped cilantro if desired.