In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese on medium speed until fluffy, 2 to 3 minutes. Gradually add the sugar, sour cream, flour, and then add in the eggs, 1 at a time, and beat well after each.
Mix in the lime juice, zest, and vanilla and beat until smooth. Pour the batter into the prepared pan.
Place the cheesecake pan in another larger pan and place in the preheated oven. Fill the larger pan halfway with hot water. Bake until slightly firm in the center, about 70 minutes.
Turn off the oven, leaving the door ajar about 8 inches (20 cm), and allow the cheesecake to cool in the oven for 1 hour. Remove from the oven and from the water bath and cool completely in the pan. If making ahead, refrigerate until ready to decorate and serve.
Remove the sides of springform pan and place the cheesecake on a serving plate.