Preheat the oven to 325°F (163°C).
In a medium bowl, combine graham cracker crumbs, 1/4 cup granulated sugar, and melted butter. Stir until the mixture resembles wet sand.
Press the crumb mixture firmly and evenly into the bottom of a 9-inch springform pan to form the crust.
Bake the crust for 10 minutes, then remove from the oven and set aside to cool slightly.
In a large mixing bowl, beat the softened cream cheese with an electric mixer on medium speed until smooth and creamy, about 2 minutes.
Gradually add 1 cup granulated sugar and continue beating until well combined and smooth.
Add eggs one at a time, beating on low speed after each addition just until combined.
Mix in vanilla extract, Greek yogurt, flour, and lemon juice until the batter is smooth and uniform.
Pour the cream cheese mixture over the cooled crust in the springform pan, spreading evenly.
Bake the cheesecake for 45 to 50 minutes, or until the center is almost set but still slightly jiggly.
Turn off the oven and leave the cheesecake inside with the oven door slightly open for 1 hour to prevent cracking.
Remove the cheesecake from the oven and cool completely at room temperature.
Refrigerate the cheesecake for at least 4 hours or overnight before removing from the springform pan and serving.