Line a 9x13-inch pan with parchment, leaving overhang for easy lifting.
Whip the cold heavy cream with powdered sugar to stiff peaks; set aside.
Beat cream cheese until very smooth, about 1 minute, scraping the bowl.
Blend in condensed milk, lemon juice, zest, and vanilla until silky.
Fold half the whipped cream into the lemon mixture until light and airy.
Spread a thin layer of lemon cream in the pan. Add a single layer of crackers.
Repeat layers of cream and crackers, finishing with remaining whipped cream on top.
Cover and chill at least 4 hours, preferably overnight, until the crackers soften.
Lift out, garnish with extra zest, slice, and serve cold.