Blend the graham crackers and sugar until it is finely ground. Add the olive oil; process until moist crumbs form. If it seems too dry, you could add a little water (or milk) a tablespoon at a time until you reach the right consistency. (If using graham cracker crumbs, you can use a bowl and wooden spoon to mix the olive oil in, with the sugar added. )
Press this mixture into a 8-inch springform pan (or pie plate); press a little up the sides to form a slight ridge. Press firmly to ensure the crust is even. Transfer to the freezer for 30 minutes.
Beat together the cream cheese, sugar, vanilla and Limoncello (or lemon juice) in a bowl until smooth; set aside.
Lightly whip the cream, and then fold it into the cream cheese mixture.
Spoon the cheesecake filling on top of the frozen graham cracker crumb base and smooth with a spatula.
Put it in the refrigerator for 3 hours or overnight.