Preheat the oven to 325°F (165°C). Grease and line an 8-inch square pan with parchment paper.
Combine the raspberries, sugar, and lemon juice in a small pot. Mash and cook over medium heat for about 5 minutes. Mix the cornstarch with water, then stir it into the berries. Cook until thickened. Let it cool.
Crush the graham crackers into fine crumbs. Mix with the melted butter, brown sugar, and salt. Press firmly into the pan. Bake for 10 minutes, then let it cool.
Beat the cream cheese, sour cream, sugar, cornstarch, salt, vanilla, lemon juice, and lemon zest on medium-low until smooth. Add the eggs and mix just until combined.
Pour the filling over the cooled crust and smooth the top. Spoon small amounts of raspberry sauce evenly over the filling. Run a chopstick, knife, or skewer through it a few times to create swirls.
Bake for about 30 minutes, until the top no longer looks wet. The center should still jiggle slightly when you move the pan.
Let it cool completely in the pan, uncovered. Refrigerate for at least 4 hours, or until firm. Slice into bars and serve chilled.