Put graham crackers in a large resealable plastic bag, and crush them with a rolling pin until very fine crumbs form.
Pour crumbs into a medium bowl; stir in sugar. Add butter, and stir until well combined.
Press the crumb mixture into a 9-inch springform pan, spreading it 1 1/2 to 2 inches up the side; press flat. Chill crust in freezer at least 10 minutes.
Meanwhile, make the filling: Using an electric mixer set at medium-high speed, beat the cream cheese in a large bowl until smooth. Beat in the condensed milk a little at a time, scraping the sides of the bowl as necessary. Beat in the lemon juice and vanilla.
Pour the filling into the crust; smooth the top with a rubber spatula. Cover with plastic wrap, and refrigerate until firm, 2 1/2 to 3 hours.