Using a fork or pastry cutter, cut the butter into the flour mixture until there are medium to large size crumbles (from the butter) in the mixture.
To the bowl, add lime juice and water. Stir together. Knead the dough a few times and form it into a round. Wrap it in plastic wrap and chill the dough in the refrigerator for an hour.
Rolling out the dough - Sprinkle flour on the rolling surface and on the rolling pin. Roll out the dough into a large circle (about 2 inches larger than the diameter of a pie pan).
Transferring the dough - Add more flour to the rolling pin and lay it on top of either the left or right edge of the dough. Roll the dough on to the rolling pin towards the opposite side, and transfer it to a parchment paper lined large cookie sheet or pizza pan.
Using a slotted spoon (so not to include the juice), transfer the mango mixture onto the center of the pie dough out to about 3 inches from the edges of the dough.
Fold in the edges of the pie dough (the edges without any filling on it) toward the middle of the galette to form a "ring" of pastry around the outside edge.
In a small bowl, whisk together egg and water to make the egg wash. Brush the egg wash around the "ring" of pastry. Sprinkle sanding sugar over the pie crust and filling.