Melt butter in a saucepan over medium heat. Whisk in flour until no lumps remain. Add apples, apple juice, sugar, brown sugar, lemon juice, and cinnamon. Cook over medium heat for 5 to 7 minutes, stirring occasionally.
Meanwhile, preheat the oven to 425 degrees F (220 degrees C).
Trim 4 circles from the pie crust; allow enough dough to fit the tin and be able to crimp and seal top and bottom crusts. Press 1 dough circle into the bottom of each of 2 mini pie tins. Add filling. Drape top crusts over filling. Wrap excess top crusts under bottom crusts edges, pressing edges together to seal. Flute the edges and cut slits in the top crusts.
Bake in the preheated oven for 15 minutes. Cover edges of crusts with strips of aluminum foil to prevent burning. Continue baking until apples are tender and crusts are golden brown, 25 to 30 minutes more.
Cool pies on rack at least 2 hours before serving.
