1/4 cup cornstarch/instant tapioca/flour (they all thicken the filling about as well, but have some subtleties in texture)
Method
Mix the flour, sugar, and salt in a large bowl.
Add the butter and rub into the flour mixture until the butter is incorporated in pea-sized chunks.
Add the water a bit at a time, combining well and making a dough that doesn't crumble. Divide in two equal-sized discs, wrap, and chill for two hours.
Preheat the oven to 400° F and flour a countertop.
Cut out a disc of parchment paper to cover the bottom of your pie pan.
Roll out the dough to a circle large enough to cover the surface of your pie pan and drape a little bit over the edge (the crust should be about 3/8" thick).
Combine the blackberries, sugar, lemon juice, lemon zest, and cornstarch/tapioca/flour in a separate bowl, then pour into the bottom pie shell in the pan.
Roll out the second disc of dough in a similar manner as the first and cut into 1/2" strips.
Cover the top of the pie with a lattice crust: put the dough strips in a stripe pattern on top of the pie, leaving about 1/2" of space between each one. Put the next set of strips on the pie perpendicular to the first set, weaving them into the top crust in an alternating over-under pattern. Do this until the top of the pie is covered.
Brush the top of the crust with the milk, then sprinkle with sugar.
Place the pie pan on a baking sheet and bake for 30 minutes.
After 30 minutes, lower the oven to 350° F, cover with a piece of aluminum foil that has a hole cut in it, and bake for another 30 minutes.
Take out of the oven and let cool for several hours before cutting.
Notes
This recipe is mostly based freehand off what my mom relayed to me for her suggestions on what ratios of ingredients would make a good pie filling; the pie crust is from online. If your pie pan is larger, you'll likely need to make more filling and patch up some of the bottom crust with the second disc.