Combine sugar and cornstarch in a large saucepan; stir in rhubarb and strawberries and bring to a simmer over medium heat. Cook until thickened, about two minutes. Remove from heat, stir in lemon juice, and let cool.
Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch pan.
Combine 3 cups flour, 1 cup sugar, baking powder, and baking soda in a large bowl. Cut in butter until mixture resembles coarse crumbs. Beat together eggs, buttermilk, and vanilla in a separate bowl. Stir egg mixture into flour until just moistened. Spoon two-thirds of the batter into prepared pan; evenly spread on the cooled filling, then cover with remaining batter.
In a small bowl, combine 3/4 cup sugar and 1/2 cup flour, and cut in butter until the mixture resembles coarse crumbs; sprinkle crumb topping over the batter.
Bake in preheated oven until topping is golden brown and a tester inserted in the center comes out clean, 45 to 50 minutes. Cool on a wire rack.