Preheat the oven to 325 degrees Fahrenheit. Line an 8x8 inch baking pan with parchment paper, leaving extra paper on the sides for easy lifting after baking.
In a bowl, mix graham cracker crumbs, melted butter, and sugar until evenly combined. Press the mixture firmly into the bottom of the prepared pan to form an even crust layer.
Bake the crust for 8 to 10 minutes until lightly set. Remove from the oven and allow it to cool slightly while preparing the filling.
In a small saucepan, combine raspberries, sugar, and lemon juice. Cook over medium-low heat until the raspberries break down into a sauce. Mash gently and allow to cool. Strain if a smoother texture is preferred.
In a mixing bowl, beat the softened cream cheese until smooth. Add sugar and mix until combined. Add eggs one at a time, mixing gently after each addition. Stir in vanilla extract.
Pour the cheesecake filling over the prepared crust and spread evenly using a spatula.
Drop small spoonfuls of the raspberry sauce over the filling. Use a toothpick or knife to swirl the sauce into the cheesecake batter to create a marbled effect.
Bake for 30 to 35 minutes, or until the edges are set and the center remains slightly soft.
Remove from the oven and allow to cool at room temperature. Transfer to the refrigerator and chill for at least 3 hours or until fully set.
Once chilled, lift the bars from the pan using the parchment paper and cut into squares before serving.