Preheat the oven to 325°F (163°C). Grease a 9x13-inch baking dish or line it with parchment paper for easy removal.
In a medium bowl, combine graham cracker crumbs, ½ cup sugar, and melted butter. Mix until well combined. Press the mixture firmly into the bottom of the prepared baking dish to form the crust.
In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy. Gradually add 1 cup of sugar and continue to mix until fully incorporated. Add the vanilla extract and mix well.
Add the eggs, one at a time, mixing on low speed after each addition until just combined. Do not overmix. Gently fold in the sour cream, flour, and lemon juice until smooth.
Pour the cheesecake batter over the crust in the baking dish and spread it evenly. Bake in the preheated oven for 30-35 minutes, or until the edges are set and the center is slightly jiggly.
Turn off the oven and leave the cheesecake bars inside for an additional 30 minutes to cool gradually. Remove from the oven and let cool to room temperature. Refrigerate for at least 4 hours, or overnight, before cutting into bars.