While crust is cooling, process 1/4 cup sugar and lemon zest in food processor small bowl until sugar is yellow and zest is broken down, about 15 sec. scraping down bowl if necessary. Transfer lemon sugar to small bowl, stir in remaining 1 1/4 cup sugar.
With mixer beat cream cheese on low to break up and sofen slightly , about 5 seconds. With machine running , add sugar mixture in slow steady stream; increase speed to medium and continue to beat until mixture is creamy and smooth, about 3 min., scraping down bowl with rubber spatula as needed.
With mixer on med-low add eggs 2 at a time; beat until incorporated, about 30 sec, scraping sides and bottom of bowl well after each addition. Add lemon juice, vanilla, and salt and mix until just incororated, about 5 sec. Add heavy cream and mix until just incorporated, about 5 sec. Give batter final scrape, stir with rubber spatula, and pour into prepared springform pan.
Fill roasting pan with enough hot tap water to come halfway up sides of springform pan. Bake until center jiggles slightly, sides just start to puff, surface is no longer shiny, and instant read thermometer inserted in center of cake registers 150 deg, approx 60 min.
With cake and water bath remaining in oven, turn off oven and prop open oven door slightly. Allow to cool for 1 hour. Transfer springform pan without foil to wire rack; run small paring knife around inside edge of pan to loosen sides of cake and cool cake to room temperature, about 2 hours.