Combine condensed milk, sour cream, half of the lemon juice, and vanilla extract in a saucepan over medium heat. Simmer and stir over medium heat until custard thickens slightly, about 5 minutes. Remove from heat and let cool, about 5 minutes. Pour into graham cracker crust.
Combine blueberry preserves, wine, and remaining lemon juice in another saucepan over medium heat; simmer and stir over medium heat until the preserves have liquefied, 3 to 5 minutes. Stir in blueberries and mulberries until coated with preserves and warmed through, about 5 minutes. Remove from heat and let cool, about 5 minutes. Pour over custard.
Bake in preheated oven until the edges of the crust are golden, about 10 minutes. Let cool on a wire rack, about 15 minutes.
Chill in the refrigerator until custard sets before serving, at least 1 hour.