In the bowl of a food processor combine butter and cream cheese and process until smooth. Add flour and salt and process just until mixture comes together to form a ball. Remove dough from the processor and shape into a disk, wrap in plastic wrap and refrigerate for at least 1 hour.
While the pie crust is chilling, prepare the crumb topping. Combine the 1/3 cup sugar, 1/2 cup flour, and the oatmeal in a small bowl and toss to combine. Add the melted butter and stir until thoroughly incorporated. Refrigerate until thoroughly chilled.
Preheat the oven to 350 degrees F.
Working on a lightly floured work surface, roll out dough out to a thickness of 1/8-inch and fit it into a 9 or 10-inch tart pan with a removable bottom. Return pie crust to the refrigerator for 20 minutes, then blind bake until lightly golden, about 18 minutes. Remove and transfer to a wire rack to cool while you assemble the strawberry filling.
Increase the oven temperature to 375 degrees F.
In a mixing bowl combine the strawberries with the sugar, lemon juice, and cornstarch and toss to combine. Spoon the strawberry filling into the prepared piecrust and spread the crumb topping evenly over the top of the filling.
Bake in the middle of the oven for 1 hour, or until filling is bubbly and crust and crumb topping are golden brown. Transfer to a rack to cool to room temperature before serving.