Combine blackberries, raspberries, and rhubarb in a medium bowl. Mix 3/4 cup sugar and 1/4 cup flour together in a separate bowl; sprinkle over fruit mixture and stir gently. Cover bowl and refrigerate for 2 hours to overnight.

Mix 2 cups flour with salt in a large bowl. Cut in shortening and 2 tablespoons butter until texture is like coarse cornmeal. Place 1/3 of mixture in a separate bowl. Add water to this mixture and mix to form a paste. Add this back to the rest of the flour and stir until a dough ball forms. Rest for 20 minutes.

Preheat the oven to 400 degrees F (200 degrees C). Roll out bottom crust and place in a 9-inch pie pan.

Mix melted butter and lemon juice into the fruit filling and spoon into the pastry-lined pie pan. Roll out the top crust, place over filling, crimp edges, and cut steam vents in the top. Brush with half-and-half and sprinkle with sugar.