Preheat oven to 450 degrees F (230 degrees C). Press pie crust into a pie plate.
Mix sugar, milk, coconut, butter, lemon juice, egg yolks, flour, and lemon zest together in a bowl. Beat egg whites in a separate bowl using an electric mixer until stiff peaks form. Lift your beater or whisk straight up: the egg whites will form sharp peaks. Fold lemon mixture into egg whites; pour into pie crust. Loosely cover the crust with aluminum foil to prevent browning.
Bake in the preheated oven for 10 minutes. Reduce oven temperature to 350 degrees F (175 degrees C) and bake until a knife inserted in the center comes out clean, about 30 minutes more. Cool pie to room temperature, at least 30 minutes; top with whipped cream.