Combine the flour, baking powder, baking soda, and salt in a large mixing bowl, set aside
Beat butter, sugar, and egg with an electric mixer on medium-high speed until fluffy, about 3-5 minutes.
Add the sour cream, lemon juice, and lemon zest and blend on medium-low until combined. Mix in the flour mixture, one cup at a time, until just combined. The dough will be very soft. Cover and refrigerate the dough for one hour.
Preheat oven to 375. Prepare baking sheet with parchment paper or cooking spray. Drop cookie dough by rounded tablespoons 2 inches apart.
Bake 10-12 minutes until edges and bottoms are golden brown. If baking two sheets at a time, rotate halfway through the baking time.
After cookies have cooled completely, make the frosting by beating all ingredients with an electric mixer for 2 minutes, until smooth. Frost the cookies and serve.