Oil an 8x8-inch baking pan, or line with parchment paper. Preheat oven to 350°F.
Place flour, oats, butter, sugar, baking powder, salt, and lemon zest in a mixing bowl and mix until well combined and crumbly. Press evenly into the bottom of the prepared pan.
In a clean bowl, whip together lemon juice, sweetened condensed milk, and softened cream cheese until smooth and creamy; fold in dried cranberries. Pour cream cheese mixture over the crust. Bake until set, about 30 minutes.
Let cool than transfer to the refrigerator to chill for at least one hour before slicing. Using a clean, warm knife for each cut will make portioning much easier.