Preheat the oven to 350°F. Lightly grease a 9×13-inch baking dish.
Peel, core, and slice the apples into 16 equal wedges.
Separate the crescent roll dough into 16 triangles.
Place one apple wedge on the wide end of each triangle and roll the dough around the apple.
Arrange the wrapped apples in the prepared baking dish with the pointed ends of the dough facing down.
In a medium bowl, mix the melted butter, granulated sugar, brown sugar, cinnamon, vanilla extract, and salt.
Spoon the butter mixture evenly over the dumplings.
Slowly pour the lemon-lime soda around the edges of the baking dish and between the rolls, avoiding the tops.
Bake for 35 to 40 minutes, until the pastry is golden brown, the apples are tender, and the sauce is bubbling.
Remove from the oven and let rest for 10 minutes before serving with the warm cinnamon sauce.