Preheat oven to 350 degrees. Line two baking sheets with parchment paper.
In a medium bowl, whisk together flour, baking soda, baking powder and salt.
In the bowl of a stand mixer, combine 1½ cups of sugar, lemon zest and cream cheese. Pour the warm butter over the cream cheese mixture and using the paddle attachment, mix to combine. Whisk in the oil, egg, milk and lemon juice until smooth. Use a rubber spatula to fold the dry ingredients into the wet, until a soft dough comes together.
Place the remaining ⅓ cup sugar for rolling in a shallow bowl. Roll two heaping tablespoons of dough into a ball between your palms, roll the ball in the sugar, and then place it on the prepared baking sheet. Space the dough balls about 2 inches apart (12 cookies per sheet).
Butter or wet the bottom of a drinking class and then dip the bottom of the glass in the remaining sugar. Gently flatten the dough balls with the bottom of the glass until they are about 2 inches in diameter, dipping the glass in sugar as necessary to prevent sticking. Sprinkle the tops of the cookies with the remaining sugar.
Bake cookies one sheet at a time, until golden brown around the edges and the centers are very lightly colored, 11 to 13 minutes. The tops will be puffy and slightly cracked. Remove cookies from oven and let cool for 5 minutes before transferring to a wire rack with a spatula.