Preheat the oven to 375°F (190°C).
Spread the pre-made pie crust in the 9-inch pie pan, crimping the edges as desired.
In a large mixing bowl, combine the fresh cranberries, granulated sugar, flour, ground cinnamon, salt, and lemon juice. Stir until well mixed.
Pour the cranberry mixture into the prepared pie crust.
Dot the top of the cranberries with small pieces of butter.
In a small bowl, whisk together the egg and milk to make an egg wash. Brush it over the top of the pie for a golden finish.
Bake the pie in the preheated oven for 45 minutes or until the cranberries are bubbly and the crust is golden brown.
Remove the pie from the oven and let it cool for at least 30 minutes before serving.
Serve the cranberry pie with whipped cream or vanilla ice cream for an extra treat.