In a large bowl, combine berries. In a small bowl, mix together white sugar and cornstarch. Gently stir sugar into berries until coated. Spoon berries into tart crust.
In a small bowl, combine flour, turbinado sugar, lemon zest, and melted butter. Sprinkle crumble topping over berries.
Bake 35 to 45 minutes, until topping is light golden brown and berry filling is bubbly. Let cool for at least 30 minutes before serving.