Preheat oven to 350°F. Line two baking sheets with parchment.
Whisk flour, baking powder, baking soda, and salt in a bowl; set aside.
Beat butter and sugar until pale and fluffy, about 2–3 minutes.
Mix in eggs, lemon zest, vanilla, and lemon juice until smooth, scraping the bowl.
Blend in sour cream just until combined.
Stir dry ingredients into the wet in two additions until no dry spots remain. Chill 15–20 minutes if the dough is soft.
Scoop 1½-tablespoon portions onto sheets, spacing 2 inches apart.
Bake 9–11 minutes until edges set and tops look matte. Cool 5 minutes on the sheet, then transfer to a rack.
Whisk confectioners' sugar with lemon juice; add milk a few drops at a time until thick and pourable.
Glaze cooled cookies and let set until the icing firms, about 20 minutes.