1. Preheat your oven to 325°F (160°C). Line a 9×9-inch baking pan with parchment paper, leaving an overhang on the sides to easily lift the bars out later.
2. In a medium bowl, combine graham cracker crumbs, 1/4 cup sugar, and melted butter. Mix until well combined, then press firmly into the bottom of the prepared pan to form the crust.
3. Bake the crust for 10 minutes, then remove from the oven and set aside to cool slightly.
4. In a large mixing bowl, beat the softened cream cheese until smooth and creamy. Gradually add in 1 cup sugar, lemon juice, and lemon zest, continuing to beat until well incorporated.
5. Add the eggs one at a time, mixing on low speed until just combined. Stir in the vanilla extract.
6. Pour the cream cheese mixture over the prepared crust and spread evenly.
7. In a small bowl, mix the pureed strawberries with cornstarch until well combined. Gently spoon dollops of the strawberry mixture over the cream cheese layer, then use a knife to swirl the mixtures together for a marbled effect.
8. Bake in the preheated oven for 35-40 minutes, or until the edges are set but the center still jiggles slightly when gently shaken.
9. Allow to cool to room temperature, then refrigerate for at least 4 hours, or overnight for best results, before slicing into bars.

My tip: Use a sharp knife to cut the bars, dipping it in hot water and wiping clean between cuts for neat edges.