Preheat the oven to 350°F.
Make the shortbread crust. In a medium bowl (or the bowl of a food processor), combine flour, sugar, lemon zest, and salt. Mix in the melted coconut oil until a wet dough forms. Press dough into an even layer in a parchment paper-lined square pan. Bake the crust for 20 minutes or until lightly golden brown, then transfer the pan to a wire rack while you make the filling.
Turn the oven temperature down to 325°F.
Make the filling. Combine the sugar and zest in a large bowl and massage the zest into the sugar with your fingers. Add in the eggs and whisk until the sugar and eggs are well combined before adding in the fresh lemon juice and the sifted flour. Whisk until smooth and pour the lemon mixture onto the warm crust.
Bake the lemon bars. Carefully place the lemon bars in the oven and bake for another 18 to 25 minutes or until the center no longer jiggles.
Let cool and cut. Cool in the pan on a wire rack for 1 hour at room temperature then cover with plastic wrap and place them in the refrigerator for another 2 hours to cool completely. Once cooled, dust with powdered sugar and cut into 9 squares, wiping the blade clean with a damp warm cloth between each cut.
Store. Store the lemon bars in an airtight container in the refrigerator for up to 3-4 days or tightly wrapped in the freezer for up to 2 months.