For the crust and streusel: Grease 9-inch pie plate. Process flour, graham crackers, and salt in food processor until finely ground. Add butter, cream cheese, and vanilla and pulse until dough forms. Remove 2 cups dough from food processor (leaving remaining dough in bowl of food processor) and turn out onto lightly floured surface. Flatten dough into 6-inch disk and transfer to prepared pie plate. Press dough evenly into pie plate and flute edges. Cover dough with plastic and refrigerate until firm, at least 1 hour or up to 24 hours.
Add oats and brown sugar to food processor with remaining dough and pulse until mixture resembles coarse meal. Transfer to bowl and use fingers to pinch topping into peanut-sized clumps; cover and refrigerate streusel.
For the filling: Adjust oven rack to lowest position and heat oven to 350 degrees. Cook 2 cups berries in saucepan over medium-high heat until juicy, about 3 minutes. Stir in sugar and lemon zest and simmer until thickened, about 5 minutes. Let cool 5 minutes, then gently toss cooked berry mixture, remaining berries, and tapioca in large bowl until combined.
Transfer berry mixture to chilled crust. Scatter oat mixture evenly over pie. Bake pie on rimmed baking sheet until fruit is bubbling around edges and streusel is browned and crisp, 45 to 55 minutes. Cool on rack 30 minutes, then refrigerate until set, at least 2 hours or up to 24 hours. Serve.