Preheat your oven to 325°F (163°C). Grease the 9x13-inch baking pan or line it with parchment paper for easier removal.
In a mixing bowl, combine the graham cracker crumbs, melted butter, and ¼ cup sugar. Mix well until the crumbs are fully moistened. Press this mixture firmly into the bottom of the prepared baking pan to form an even layer.
In another mixing bowl, beat the softened cream cheese and ¾ cup sugar together using an electric mixer until smooth and creamy. Add the eggs, one at a time, mixing well after each addition. Then add the vanilla extract and lemon juice, mixing until just combined.
Pour the cheesecake filling over the crust, spreading it evenly. Set this aside while you prepare the raspberry swirl.
In a small saucepan over medium heat, combine the raspberries, 2 tablespoons of sugar, and 1 teaspoon of lemon juice. Cook for about 5-7 minutes until the raspberries break down and the mixture thickens slightly. Remove from heat and let cool slightly.
Dollop the raspberry mixture over the cheesecake layer. Using a knife or the tip of a spatula, gently swirl it into the cheesecake filling to create a marbled effect.
Bake in the preheated oven for 40-45 minutes, or until the cheesecake is set and only slightly jiggles in the center.
Once done, remove from the oven and allow it to cool at room temperature for about 1 hour. Then, refrigerate for at least 3 hours (or overnight) before slicing into bars.
Cut into 12 equal pieces and serve chilled or at room temperature. Enjoy!