Preheat oven to 350°F. In electric mixer, beat softened cream cheese and granulated sugar at high speed until fluffy, about 3 minutes. Add eggs and beat until blended, about 1 minute. Add evaporated milk and lime juice, then mix at low speed until blended. Pour batter into crust and bake until set in center, 35 to 40 minutes. Let cool on rack for 20 minutes, then chill until cold, about 1 hour.
Right before serving: Beat cream, confectioners' sugar and vanilla extract in an electric mixer, until stiff enough to spread. Serve cream on top of pie.