Whisk together flour, baking soda, baking powder, and salt in a medium bowl.
In a large bowl, beat butter, cream cheese, and 1¼ cups sugar until smooth and creamy, 1 to 2 minutes.
Mix in vanilla, lemon juice, and lemon zest.
Beat in the egg.
Slowly add flour mixture, mixing in a little at a time, until just combined.
Wrap with plastic wrap and refrigerate for 1 hour.
Preheat the oven to 350°F and line a baking sheet with parchment paper.
Scoop sugar cookie dough into balls and roll in sugar until coated all over.
Bake cookies for 10 minutes, until the edges just start to brown.
Let cookies cool on the baking sheet for 5 minutes and move to a wire rack to finish cooling.