Prepare the Sugar Cookie Base:

1. Preheat your oven to 350°F (175°C). Grease a 9-inch springform pan with butter or non-stick spray.
2. In a large bowl, mix the sugar cookie mix, softened butter, and egg until a soft dough forms.
3. Press the dough evenly into the prepared pan, pressing it up the sides about 1 inch.
4. Bake for 12-15 minutes or until the edges are lightly golden. Remove from the oven and let it cool completely.

Make the Cheesecake Filling:

1. Reduce the oven temperature to 325°F (165°C).
2. Beat the softened cream cheese in a large mixing bowl until smooth and fluffy.
3. Gradually add the granulated sugar and powdered sugar, beating until fully incorporated.
4. Mix in the sour cream, vanilla extract, and lemon juice or zest (if using).
5. Add the eggs one at a time, mixing on low speed until just combined. Do not overmix.

Assemble and Bake:

1. Pour the cheesecake filling over the cooled sugar cookie base, smoothing the top with a spatula.
2. Bake in the preheated oven for 55-65 minutes, or until the edges are set and the center jiggles slightly when gently shaken.
3. Turn off the oven and leave the cheesecake inside with the door ajar for 1 hour to cool gradually.
4. Remove the cheesecake from the oven and let it cool completely at room temperature. Refrigerate for at least 4 hours, preferably overnight, before serving.

Serve:
Carefully remove the cheesecake from the springform pan. Slice and serve plain or with toppings like fresh berries, whipped cream, caramel drizzle, or powdered sugar for extra flair.