Preheat oven to 350℉.
In a small sauce pot over low heat, add raspberries and sugar. Gently mash berries with a fork and mix with sugar for about 3 minutes, until it reaches the consistency of a runny preserve. Let cool.
In a food processor, pulse crackers and sugar until fine crumbs. Place in a bowl and mix together with melted butter, using a fork.
Using your fingers, press graham cracker crust evenly into the bottom of a 9 x 13 baking dish.
Bake crust for 10 minutes, then remove from oven and let cool for a few minutes.
Using a KitchenAid stand mixer with flat beater attachment or a handheld electric mixer, add cream cheese, sugar, and lemon zest, and mix well. Next, add sour cream, lemon juice, flour, and vanilla extract, and mix again. Lastly, add eggs and mix until smooth.
Pour cheesecake mixture on top of graham cracker crust and spread out evenly using a rubber spatula. Add spoonfuls of raspberry mixture in several places on top of cheesecake and swirl using a chopstick.
Bake for 35 minutes. Refrigerate for at least 2 hours before serving.
Tip: Cut and serve cheesecake bars using a thin flat metal spatula.