Place the butter in freezer for 20 minutes.
In a food processor add the flour, salt and sugar and pulse a couple times.
Add the butter to the food processor and pulse a few times until the mixture resembles peas. Add the ice water one tablespoon at a time and continue pulsing. The dough should start to hold together.
Remove dough from food processor and place it over your working surface. Form the dough into 2 discs, cover in plastic wrap and refrigerate for at least one hour up to 2 days before using.
Peel, core and slice the pears and toss with the lime juice.
In a sauce pan, add the 1/2 cup of butter and melt over medium heat. Add the flour and mix until the mixture turns into a thick paste. Add water, white sugar, brown sugar and cinnamon and continue stirring. Let it simmer for a couple minutes.
Preheat oven to 425 F degrees.
Take out the pastry discs from the fridge and roll out a disc so that it's 12 inches in diameter and place it and arrange in your pie dish. Brush the pie crust with egg white so that it doesn't get soggy.
Add the pears to the pie dish and pour the caramel sauce over the pears, you don't have to pour it all if you think it's too much sauce. Roll out the other disc so that it's 12 inches in diameter as well and cut it into lattice strips. Arrange the lattice strips nicely over the pears and brush with remaining egg white.
Bake for 45 minutes or until golden brown.
Let it cool before serving.