Preheat the oven to 350℉.
In a large bowl, combine the shredded chicken with ¼ cup of the lime juice and the chopped cilantro. Mix gently to coat the chicken evenly.
In a separate wide-mouth bowl, stir together the alfredo sauce, enchilada sauce, and remaining ¼ cup lime juice until fully combined.
To assemble, dip each tortilla in the sauce to coat both sides, then place it (folded but open) in a greased baking dish.
Spoon about ½ cup of the chicken filling down the center of each tortilla and roll it up. Continue with all the tortillas and filling.
Pour the remaining sauce over the rolled enchiladas. Use a spatula to gently lift each one, allowing sauce to seep underneath.
Sprinkle the shredded cheese evenly over the top and cover the dish with foil.
Optional Make-Ahead: At this stage, you can refrigerate the enchiladas until ready to bake, or freeze them in a well-covered dish for later.
Bake covered for 30 minutes. Remove foil and bake for an additional 15–20 minutes, until the cheese is melted and golden and the sauce is bubbling.
Garnish with fresh cilantro and lime wedges before serving.