In the bowl of an electric mixer, beat the cream cheese on low speed for 1 minute until smooth and free of any lumps. Add the eggs, 1 at a time, and continue to beat slowly until combined. Gradually add sugar and beat until creamy, for 1 to 2 minutes.
Add sour cream, lemon zest, and vanilla. Periodically scrape down the sides of the bowl and the beaters. The batter should be well-mixed but not over-beaten. Pour the filling through a fine strainer into the crust-lined pan and smooth the top with a spatula.
Set the cheesecake pan on a double layer of aluminum foil and fold up the sides around it. Place the cake pan in a large roasting pan. Pour boiling water into the roasting pan until the water is about halfway up the sides of the cheesecake pan; the foil will keep the water from seeping into the cheesecake. Bake for 30-45 minutes. The cheesecake should still jiggle (it will firm up after chilling), so be careful not to overcook. It is done when the center is 150 degrees. Let cool in pan in the oven with the door cracked for 30 minutes. Remove and cool on a rack until room temp. Chill in the refrigerator, loosely covered, for at least 4 hours or preferably overnight. Loosen the cheesecake from the sides of the pan by running a thin metal spatula around the inside rim.