Reduce oven to 160 ℃ (320 ℉). In a medium bowl, beat the cream cheese, sour cream, powdered sweetener, lemon zest, and lemon juice until smooth.
Beat in the eggs, one at a time.
Finally, add in the vanilla extract.
Pour the filling over the crust and bake for 50 minutes. The top should be slightly hardened but the centre should still be jiggly. Turn the oven off. Leave the cheesecake in the oven, with the door slightly open, for 2 hours or until cooled completely (this will prevent the cake from cracking).
Place in the fridge for 4 hours to chill.