Preheat the oven to 350°F (175°C). Lightly grease a 9×13-inch baking dish and set aside.
Open the crescent roll cans and carefully separate the dough into individual triangles.
Spoon a small amount of apple pie filling onto the wide end of each triangle. Do not overfill.
Starting at the wide end, gently roll the dough toward the pointed end, enclosing the filling. Place each dumpling seam-side down in the prepared baking dish.
In a medium bowl, mix the softened butter and brown sugar together until well combined.
Spoon a small amount of the butter mixture over the top of each dumpling, spreading lightly.
Slowly pour the lemon-lime soda into the baking dish, pouring it around the dumplings rather than directly on top.
Bake uncovered for 35–45 minutes, or until the dumplings are golden brown and the sauce is bubbling.
Allow to cool slightly before serving. Spoon some of the sweet sauce from the pan over each dumpling when serving.
Enjoy!