Preheat your oven to 325°F (163°C) and line a muffin tin with paper liners. In a medium bowl, mix together graham cracker crumbs, granulated sugar, and melted butter until well combined. Firmly press this mixture into the bottom of each liner to form a crust. Bake for 5 minutes until lightly golden, then remove from the oven and let them cool while you prepare the filling.

In a large mixing bowl, beat the softened cream cheese and granulated sugar together until smooth and creamy. Add sour cream, vanilla extract, and fresh lemon juice, mixing until everything is well incorporated. Gradually crack in the room temperature egg and blend just until the mixture is uniform.

Spoon the cheesecake filling into each cooled graham cracker crust, filling each liner about ¾ full. Place the muffin tin in the preheated oven and bake for 18-20 minutes. The edges should be set, while the centers remain slightly jiggly. After baking, cool the mini cheesecakes in the pan for 10 minutes before transferring them to a wire rack to cool completely.

In a medium saucepan over medium heat, combine raspberries, water, granulated sugar, and cornstarch. Stir continuously until the mixture thickens, about 5-7 minutes. Once thickened, remove from the heat, stir in the lemon juice, and allow it to cool completely.

Once the mini cheesecakes are chilled and firm, gently spoon the cooled raspberry topping over each one. These delightful Raspberry Mini Cheesecakes are now ready to be served.