Arrange oven racks to divide in thirds. Preheat to 350°F. Grease cookie sheets.
In large bowl of stand mixer, cream butter and sugar. Add egg; beat well to combine. Add lemon juice and zest and vanilla; mix until incorporated.
Add salt, baking powder, and flour; mix until dough is uniformly mixed.
Use teaspoon to form 1 inch balls; place 2 inches apart on greased cookie sheet. Bake 8 - 10 minutes, until edges are lightly golden.
Meanwhile, using small bowl, combine glaze ingredients. Whisk until smooth, adding additional lemon juice, until it is a spreadable consistency.
When cookies are done, allow cookies to cool 1 - 2 minutes before removing to a cooking rack. While still hot, spread each cookie with glaze. Allow to cool completely before serving.