Cook the raspberries, sugar and lemon juice in a small saucepan over medium heat for 6 to 8 minutes, mashing the berries, until thick and jammy. Press through a fine mesh strainer to remove the seeds and let the sauce cool completely.
Preheat the oven to 350°F and line a 9x9-inch baking pan with parchment, leaving an overhang on two sides. Mix the graham cracker crumbs, sugar and melted butter, press into the pan and bake for 10 minutes.
Reduce the oven to 325°F and place a pan of hot water on the lower rack. Blend the cottage cheese in a food processor or blender for 2 to 3 minutes, scraping down the sides, until completely silky.
Add the cream cheese, sugar, cornstarch, vanilla, lemon zest and salt and blend until smooth. Add the eggs and pulse just until combined.
Pour the batter over the crust and spread it evenly. Drop small spoonfuls of the raspberry sauce over the top and drag a skewer through them to create a marbled pattern.
Bake on the middle rack for 40 to 50 minutes, until the edges are set and the center has a slight wobble.
Cool completely in the pan, then refrigerate for at least 4 hours. Lift out using the parchment and cut into 16 bars.