Stir graham cracker crumbs, melted butter, and sugar in a bowl until the texture of wet sand. Press firmly into the bottom of a 9-inch springform pan using the bottom of a measuring cup. Chill while you make the filling.

Combine 8 oz blackberries, sugar, and water in a small saucepan. Cook over medium heat for 6-8 minutes, mashing berries occasionally, until syrupy and broken down. Press through a fine mesh sieve into a bowl to remove seeds; you should have about 1/2 cup smooth sauce. Cool completely. Reserve remaining 4 oz fresh berries for topping.

Beat cream cheese, powdered sugar, vanilla, and lemon zest with an electric mixer on medium speed until completely smooth and fluffy, about 3 minutes. Scrape the bowl twice to eliminate lumps.

In a separate bowl, whip cold heavy cream on medium-high speed until stiff peaks form, about 3-4 minutes. The cream should hold its shape when you lift the beaters.

Gently fold half the whipped cream into the cream cheese mixture to lighten it, then fold in the remaining cream until no streaks remain. Do not overmix or the filling will deflate.

Spread half the filling over the chilled crust. Drizzle 3 tablespoons of the cooled blackberry sauce over the surface, then use a knife to swirl gently. Spread remaining filling on top. Drizzle with remaining sauce and swirl again. Tap the pan firmly on the counter twice to release air bubbles.

Cover loosely with plastic wrap and refrigerate at least 4 hours, preferably overnight, until completely firm. The center should feel set when gently pressed. Run a thin knife around the edge before releasing the springform. Top with reserved fresh berries just before serving.