Preheat oven to 350 degrees. In a medium bowl, whisk together flour, baking soda, salt, and lemon zest. In a large bowl, using an electric mixer, beat butter and granulated sugar until light and fluffy. Add egg, vanilla, and lemon juice and beat until combined. With mixer on low, beat in flour mixture.
Drop dough by heaping tablespoons, 1 inch apart, onto two baking sheets. Bake until edges are golden, 15 to 20 minutes, rotating sheets halfway through. Let cool 2 minutes on sheets, then transfer cookies to a wire rack to cool completely. Spread cookies with Lemon Glaze and let set, about 1 hour.
Always zest the lemons (preferably with a Microplane tool) before juicing them. For orange- or lime-flavored cookies, substitute the zest and juice of those fruits.