Preheat over to 325 degrees F. Grease a 9-inch springform pan and line the bottom with parchment paper. Wrap the outside of the pan with foil to prevent water from getting in from the water bath. (Maybe even use a double layer of foil.)
In a medium mixing bowl, stir together graham cracker crumbs, melted butter, and ⅓ cup granulated sugar until thoroughly combined.
Press graham cracker mixture into the springform pan, creating a thick, even layer across the bottom and about halfway up the sides of the pan. Pack down the crumbs so that the crust holds together. Set aside.
In a medium mixing bowl, beat the cream cheese with a hand mixer (or stand mixer) until light and fluffy. Add 1 cup of granulated sugar and continue beating for 1 minute.
Add flour, lemon extract, and vanilla extract to the mixture and combine. Beat in sour cream, heavy cream, lemon zest, and lemon juice. Mix just until combined.
By hand, mix in the eggs, one at a time. Stir gently to prevent extra air from getting into the mixture. Pour cheesecake mixture into the prepared graham cracker crust and spread the top smooth.
Place the pan into a larger vessel that can hold water at least 1-inch of water up the sides of the pan. Fill with water to create a water bath for the cheesecake.
Bake for 45 minutes. After 45 minutes, turn off the oven, keeping the door closed for 20 minutes. After this 20 minutes, crack the oven door and leave the cheesecake in place for another 20 minutes.
Remove the cheesecake from the oven. Remove from the water bath, and allow to cool on a wire rack to room temperature. Then transfer to the refrigerator to chill for at least 2 hours to overnight.
Top with dollops of whipped cream, fresh berries, and lemon slices for garnish. Cut into slices and serve.
Notes
Store any leftovers covered in the fridge for up to 5 days or freeze for up to 1 month.