Preheat oven to 350 degrees F (175 degrees C). Line a rimmed baking sheet with aluminum foil; coat with cooking spray.
Combine chicken, barbeque sauce, lime juice, cumin, and chili powder in a saucepan over medium heat. Reduce heat and simmer, stirring occasionally, until chicken is heated through, about 10 minutes. Remove from heat.
Spread a single layer of tortilla chips on the prepared baking sheet. Top with 1/2 the chicken mixture and 1 1/4 cups Cheddar cheese. Place another layer of tortilla chips over cheese and top with remaining chicken mixture and cheese.
Bake in the preheated oven until Cheddar cheese is melted and golden brown, about 10 minutes.