1. For the pastry, cut the lard into pieces. Combine the flour, sugar, and salt in a bowl. Cut the lard and shortening into the dry ingredients with a pastry blender, until mixture resembles a coarse meal.
2. Lightly beat 1 egg with the vinegar and 1 tablespoon of the cold water and add it to the bowl, tossing with a fork. Add water, a tablespoon at a time, until dough just holds together. divide the dough in half, wrap in plastic, and refrigerate for 1 hour.
Filling:
Combine half of the walnuts and all remaining filling ingredients, except the 1 tbsp. granulated sugar, in a bowl and mix well. Set aside.
COOKING:
1. Butter a fluted tart pan with a removable bottom.
2. In a small bowl, lightly beat the remaining egg with 1 tablespoon cold water.
3. On a lightly floured work surface, roll out one portion of dough into a circle and ease it into the tart pan. Trim the edge, leaving a 1/2 -inch border, and brush edge of crust with egg. Pour filling into the crust and pack it evenly with the back of a spoon. Roll out the remaining dough into a square. With a sharp knife, cut dough into 10 strips.
4. To form the lattice, put 5 strips horizontally across the top of the tart at 1-inch intervals. Working carefully, weave 5 vertical strips over and under the horizontal strips, taking care not to break the strips as you work. Trim and flute the edge. Brush the pastry with egg. Sprinkle walnuts in the spaces between the latticework and dust the top of the pie with the remaining tablespoon granulated sugar.
5. Adjust oven rack to middle position and heat oven to 425F. Put the pie on a foil-lined baking sheet and bake for 15 minutes. Reduce heat to 350F and bake until crust is golden and filling is bubbling, about 35 minutes. Serve at room temperature.

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