Preheat oven to 350°F.
Place flour in the bowl of a food processor fitted with the steel blade. Distribute chilled butter cubes over the flour. Pulse 12 times.
Drizzle water over the flour/butter mixture and pulse until dough begins to clump around the base of the blade.
Remove the dough and place it on a lightly floured board.
Briefly knead into a ball, then flatten to a disc and, using a floured rolling pin, roll into an 11-inch round, about 1/8-inch thick.
Place the dough in a deep 9-inch pie plate and trim the edges, then crimp. Place in the refrigerator while you make the filling.
Wash the Meyer and Lisbon lemons well. Cut the Meyer lemon in half lengthwise, then cut each half lengthwise. Cut the quarters into 1/4-inch slices. This will allow you to remove all the seeds.
Using a micro plane or box grater, finely grate the zest of the Lisbon lemon. Reserve the rest of the Lisbon lemon for another use.
Place the Meyer lemon pieces (with skin) in a blender along with the grated zest. Add the eggs, butter, vanilla, Fiori di Sicilia, and sugar. Blend until smooth.
Pour the mixture into the unbaked pie crust and bake for 40 minutes or until set.
Let the pie cool, then chill in the fridge or serve at room temperature.