Heat oven to 350°F and arrange a rack in the middle. Grease a 7 x 11-inch baking dish and set aside.
Combine fruit, cornstarch, sugar, lavender, and lemon juice in a medium bowl and stir until cornstarch and sugar have coated the fruit.
Crumble two-thirds of the dough in the bottom of the baking dish. Spread fruit mixture evenly over the dough and then crumble remaining dough on top, covering evenly.
Bake until fruit is bubbly and top is golden brown, about 1 hour. Let sit at least 30 minutes before serving with ice cream and an extra sprinkling of lavender buds.