Line a 9" Springform pan with parchment paper (optional for easy removal).
Combine graham cracker crumbs and butter, then press into the bottom and about 1/2" up the sides of the pan.
Beat the cream cheese in a large bowl with an electric mixer until smooth.
Add powdered sugar, lemon juice, lemon zest, and vanilla, then beat until smooth.
In a separate bowl, beat heavy cream on high until stiff peaks form, then gently fold into the cream cheese mixture.
Taste and adjust sweetness or lemon flavor with extra sugar or zest if desired.
Pour filling into the crust, cover, and refrigerate for at least 6 hours or overnight. Serve with sweetened whipped cream.