Make the filling: Beat the cream cheese and sugar in a large bowl with a mixer on medium-high speed until smooth and slightly fluffy, about 3 minutes. Beat in the eggs, one at a time, then beat in the lemon juice and vanilla. Pour the batter into the prepared crust. Transfer to the oven and bake until the edges are set but the center still jiggles slightly, 1 hour to 1 hour, 10 minutes. Turn off the oven and keep the cheesecake in the oven with the door ajar, 20 minutes. Remove from the oven and run a knife around the edge of the cake to loosen. Transfer to a rack; let cool completely, then refrigerate until set, at least 4 hours or overnight.