Preheat oven to 350 degrees with rack in the center.
Combine graham cracker crumbs, sugar and melted butter in a medium sized bowl until moistened. Pour inside the spring form pan and evenly spread throughout bottom of the pan and about 1-inch up the sides pressing gently using your hands. Place in the oven and bake for 10 minutes. Remove and set aside to cool.
Combine and rinse raspberries, blueberries, and blackberries in a colander and set aside to drain completely. Gently pat dry if needed. (Do not crush berries) Set aside. NOTE: If you are a berry lover and want to enjoy a mouthful of berries in every bite, you may add up to 24 ounces total. However, it may not look as pretty because the berries will start to run. If you don’t mind a little imperfection, feel free to take this route.
Whisk sweetened condensed milk, egg yolks, heavy whipping cream and vanilla in a medium mixing bowl. Whisk in lemon juice and lemon zest until well combined.
Pour 1/3 of the filling onto the cooled crust. Sprinkle half of the mixed berries to cover. Pour another 1/3 of the custard filling, sprinkle the remaining berries then top with the remaining third of the filling. Gently spread the filling to cover the top or move pan from side to side to distribute evenly if needed. Bake for 30-35 minutes until just set.
Remove from oven and cool to room temperature. Cover and refrigerate until completely cold, about 3-4 hours or overnight. Carefully run a hot knife around the cake to remove from the spring form pan. Leave the bottom of the spring form pan attached to serve or carefully transfer to a serving platter if preferred. Slice and serve.