Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large mixing bowl, beat together the softened butter and 3/4 cup granulated sugar using an electric mixer until the mixture is light and fluffy.
Add the egg and sour cream to the butter mixture and beat until well combined.
Stir in the freshly squeezed lemon juice and finely grated lemon zest, mixing until evenly distributed.
In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Be careful not to overmix.
Gently fold in the cut gumdrops, ensuring they are evenly distributed throughout the dough.
Using a tablespoon or cookie scoop, drop dough balls onto the prepared baking sheet. Roll each ball in the remaining 1/4 cup granulated sugar before placing them on the sheet.
Bake for 10-12 minutes, or until the edges are lightly golden. The centers may still look a bit soft, but they will firm up as they cool.
While the cookies are cooling, whisk together the warmed lemon juice for the glaze. Drizzle over the cooled cookies for a sweet finish.