Preheat your oven to 325°F. Line an 8-inch square baking pan with parchment paper or foil, leaving overhang on two sides.
In a bowl, combine the graham cracker crumbs, sugar, and melted butter. Mix until evenly moistened.
Press the mixture firmly into the bottom of the prepared pan to form an even crust.
Bake the crust for 10 minutes, then remove and let cool slightly. Keep the oven at 325°F.
In a large mixing bowl, beat the softened cream cheese until smooth and creamy.
Add the sugar, lemon zest, lemon juice, and vanilla. Mix until fully combined, scraping down the bowl as needed.
Add the eggs one at a time on low speed, mixing just until incorporated.
Pour the cheesecake filling over the cooled crust and smooth the top.
In a blender or food processor, blend the raspberries and sugar until smooth. Strain through a fine mesh sieve to remove seeds.
Spoon small dollops of raspberry puree over the cheesecake filling.
Use a knife to gently swirl the raspberry into the surface.
Bake for about 35 minutes, until the top is set and the center no longer looks wet.
Let the cheesecake cool completely at room temperature, then refrigerate for at least 3 hours or overnight.
Lift from the pan using the overhang, slice into squares, and serve chilled.