Preheat oven to 350 degrees F. Line 2 baking sheets with parchment sheets and set aside.

In a small mixing bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

Place the 1 1/3 cups sugar and cream cheese in a large mixing bowl. Using a metal whisk, stir until combined. Pour the melted butter over the mixture, then add the vegetable oil, egg, lemon zest, milk, and lemon juice. Whisk until combined. Stir in the flour mixture with a silicone spatula until the dough is cohesive and smooth (it will be very moist.)

Using a standard cookie scoop (which is 1 1/2 tablespoons), generously scoop the dough (you want about 2 tablespoons of dough per cookie) and roll into the reserved sugar. Evenly space 12 cookie balls on the sheet and repeat with the other baking sheet. If desired, sprinkle cookies with remaining sugar. Bake for 6 minutes. Rotate the pan and bake for another 5-6 minutes or until set around the edges. Repeat with the second pan. Allow the cookies to cool for about 5 minutes on the pan and then transfer to a cooling rack.