Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a mixing bowl, cream together the butter and sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined.
In another bowl, whisk together the flour, baking soda, ground ginger, ground cinnamon, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Roll the dough into small balls and place them on the prepared baking sheet. Flatten each ball slightly with the back of a spoon.
Bake for 8-10 minutes, or until the edges are golden brown. Let the cookies cool on the baking sheet for a few minutes before transferring to a cooling rack.
While the cookies are cooling, prepare the icing by mixing the powdered sugar and lemon juice until smooth.
Once the cookies are completely cool, drizzle the lemon icing over the top.