(1) Make the Pie Crust:

1. Preheat and Grease: Preheat the oven to 425F and grease a pie pan with a removable bottom.
2. Prepare the Pie Crust Dough: In a large mixing bowl, whisk the gluten-free flour and sugar until fully combined. Add chilled coconut oil and cut the coconut oil into the flour (either with a pastry cutter, two knives, or use the back of a fork to press the coconut oil into the flour). You’ll get an off-white crumbly mixture with the texture of coarse sand. Add the beaten egg and mix well. The mixture will still be crumbly, but will be slightly pale yellow now. Add cold water 1 tablespoon at a time, mixing with a spoon until you get a dough that holds together (better to have a dough that’s a little too moist than too dry).
3. Roll out Dough: Shape dough into a disc and then roll out the dough between two pieces of parchment paper until the dough is slightly larger than your pie tin.
4. Press Dough into Pie Tin: Remove the top parchment paper and then place your hand below the bottom piece of parchment to flip the dough onto your pie tin, then slowly peel off the remaining parchment paper as you press the dough into the tin. Note that the dough may break, but don’t worry as you can easily press the dough back into place (it will still look beautiful once baked).
5. Par-Bake the Crust: Brush the exposed edges with egg wash, and then bake the crust for 20 minutes at 425F until the crust is firm and the edges are golden brown. Once done, remove from the oven and let cool.
   

(2) Prepare the Lemon Curd:

1. Cook the Lemon Curd: While the crust is par-baking, prepare the curd. Combine the sugar and eggs together in a large microwave-proof bowl, and whisk well until combined. Add the lemon juice, zest, and melted coconut oil together and mix well. Cook the mixture on high heat in the microwave for 1-minute intervals, whisking well after each minute. This should take between 3 to 7 minutes, depending on the strength of your microwave. You’ll know the lemon curd is ready once the mixture is thick and coats the back of a metal spoon.
2. Strain the Curd: Strain the lemon curd through a fine-mesh strainer to ensure that it becomes as smooth and silky as possible. Let the curd cool for at least 10 minutes.

(3) Make the Meringue:

1. Make the Syrup: Combine sugar and water in a medium pot, stirring over low heat until sugar is totally dissolved. Once dissolved, turn heat on to high until the syrup comes to a boil.
2. Whisk Egg Whites: Meanwhile, whisk egg whites with a hand mixer in a heat-proof bowl until you get firm peaks (about a few minutes). Let syrup boil until it reaches 240F, before pouring the hot syrup into the whipped egg whites, mixing continuously until incorporated and the bottom of the bowl has cooled and the meringue has reached room temperature. 

(4) Assemble and Finish Baking the Lemon Meringue Pie:

1. Preheat Oven: Preheat oven to 350F and arrange rack to lower-third position.
2. Fill the Crust: Fill the par-baked pie crust with the cooled lemon curd.
3. Spread Meringue Over Lemon Curd: Scoop the meringue over the lemon curd and gently spread it evenly all over. Use the back of a large spoon to make decorate peaks.
4. Bake: Bake the pie for 25 to 30 minutes until the peaks of the meringue are brown. If the meringue is browning too much, tent the pie gently with aluminium foil.
5. Cool Completely: Once the pie is baked, remove it from the oven let it cool on a cooling rack for at least 1 hour until it comes to room temperature. Chill the lemon meringue pie for at least 4 hours (or better yet, overnight) before slicing and serving.