Combine 2/3 cup sugar and cornstarch in a large saucepan; stir in rhubarb and strawberries. Bring to a simmer over medium heat; cook until thickened, about 2 minutes. Remove from the heat, stir in lemon juice, and let cool.

While the filling cools, preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch baking dish.

Combine 3 cups flour, 1 cup sugar, baking powder, and baking soda in a large bowl. Cut in 1 cup cold butter using 2 knives or pastry blender until the mixture resembles coarse crumbs.

Whisk buttermilk, eggs, and vanilla together in a separate bowl; stir into flour mixture until just moistened. Spoon 2/3 of batter into the prepared pan; spread cooled filling over top, then cover with remaining 1/3 of batter.

Combine 3/4 cup sugar and 1/2 cup flour in a bowl. Cut in 1/4 cup cold butter using 2 knives or pastry blender until the mixture resembles coarse crumbs; sprinkle over batter.

Bake in the preheated oven until topping is golden brown and a tester inserted into the center comes out clean, 45 to 50 minutes. Cool on a wire rack.