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For the crust:
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Measure the lard or coconut oil, then place in the freezer to chill for about 30 minutes.
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Dice the cold fat and butter and place in the refrigerator to keep cold.
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Combine the flour, sugar, and salt in a food processor fitted with the steel blade or in a large bowl. Add the cold fats and, if you're mixing by hand, use a pastry cutter to cut them into the dry ingredients. Or, use the pulse setting on the food processor for approximately 30 pulses. Either way, you want to cut the ingredients together until the mixture looks like coarse crumbs with a few pea-sized bits.
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If you used the food processor, transfer the mixture to a large bowl. Drizzle in the ice-cold water and use the straight edge of a rubber spatula to cut the water in. When it begins to come together, press down with the broad, flat surface of the spatula. Finally, use your hands to gently fold the mixture without kneading it until the dough barely holds a ball shape with a few shaggy bits on the bottom of the bowl.
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Shape into a disk and wrap in plastic wrap. Chill for at least 30 minutes or up to 3 days in the refrigerator.
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Lightly dust a surface with flour, then place the chilled dough disk on the flour. Dust the top of the disk lightly, as well. Roll the dough out, starting in the middle of the disk and rolling toward the edges. Be sure to flip the dough over every few strokes to prevent sticking; this will allow you to use less flour and disrupt the balance of ingredients as little as possible. Roll until you are left with a circle about an inch wider in diameter than the top of your 9-inch pie dish. Lay the dough disk in the pie dish, pressing the edges in and down, rather than stretching from the center up. Fold the edges of the dough under, building them up about a quarter inch above the rim of the dish. Flute the edges as desired, then transfer the crust to the refrigerator for 30 minutes.
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Preheat the oven to 375 F. Use a fork to poke holes in the bottom of the crust. Cut a square of parchment to fit the pie crust and set it inside. Fill the parchment with dried beans or metal pie weights and bake for 15 minutes. Remove the parchment and weights and bake the crust for 15 minutes more or until it is golden and firm to the touch. Let it cool completely.
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For the filling:
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Place 8 ounces of the strawberries, lime juice, and sugar in a blender and process until smooth. Pour the mixture through a fine mesh sieve into a medium bowl.
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In a small bowl sprinkle the gelatin over the cold water and allow to soften for five minutes. Add the hot water to the gelatin and whisk to melt. Pour the gelatin mixture into the strawberry mixture and whisk to combine.
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Use the remaining pound of strawberries to fill the cooled pie crust. Slice the large berries and leave the small ones whole. Pour the gelatin mixture over the berries up to the top of the crust. Cover the pie with plastic wrap and chill until firm, about three hours.
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For the topping:
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In the bowl of a stand mixer fitted with the whisk attachment or by hand, whip the cream, vanilla, and sugar to soft peaks. Top the pie and serve chilled.
