Prepare the Raspberry Swirl : In a small saucepan, combine the raspberries and 1 tablespoon of sugar. Cook over medium heat, stirring frequently, until the berries break down and form a sauce (about 5 minutes). Strain the mixture through a fine-mesh sieve to remove the seeds, leaving a smooth raspberry sauce. Set aside to cool.
Make the Crust : Preheat your oven to 325°F (165°C). Grease a 9-inch springform pan or line the bottom with parchment paper. In a medium bowl, mix the graham cracker crumbs and melted butter until evenly combined. Press the mixture firmly into the bottom of the prepared pan. Bake for 8-10 minutes, then set aside to cool.
Prepare the Cheesecake Filling : In a large mixing bowl, beat the softened cream cheese and sugar until smooth and creamy. Add the sour cream, lemon juice, and lemon zest, mixing until fully incorporated. Beat in the eggs, one at a time, on low speed to avoid overmixing.
Assemble the Cheesecake : Pour the cheesecake batter over the cooled crust, spreading it evenly. Drop spoonfuls of the raspberry sauce onto the batter. Use a skewer or knife to swirl the raspberry sauce into the batter, creating a marbled effect.
Bake the Cheesecake : Place the springform pan in a larger baking dish. Fill the dish with about 1 inch of hot water to create a water bath, which helps prevent cracks in the cheesecake. Bake the cheesecake for 55-65 minutes, or until the edges are set but the center is slightly jiggly. Turn off the oven and leave the cheesecake inside with the door slightly ajar for 1 hour.
Chill and Serve : Remove the cheesecake from the oven and water bath. Let it cool to room temperature, then refrigerate for at least 4 hours or overnight. Before serving, run a knife around the edges of the pan to release the cheesecake. Garnish with fresh raspberries or lemon zest, if desired.