Preheat oven to 350°F (175°C) and line an 8x8 inch baking pan with parchment paper.
Combine graham cracker crumbs, 1/4 cup sugar, and melted butter in a bowl. Press firmly into the bottom of the prepared pan.
Bake the crust for 10 minutes, then remove from the oven and set aside.
In a large bowl, beat the cream cheese and 1/2 cup sugar until smooth. Add 2 eggs and vanilla extract, mixing until just combined.
Spread the cream cheese mixture evenly over the pre-baked crust.
In a separate bowl, whisk together the remaining 1 cup sugar, 2 eggs, lemon juice, lemon zest, and flour until well blended.
Slowly pour the lemon mixture over the cream cheese layer.
Bake for 30 to 35 minutes, or until the edges are golden and the center is set.
Allow to cool to room temperature, then refrigerate for at least 4 hours before slicing into bars.