Preheat the oven to 350 degrees and line a cookie sheet with parchment paper and set aside.
Using a medium bowl, whisk together the flour, baking soda and salt.
Using a standing mixer, beat the butter and sugar until creamy and fluffy.
On medium speed, beat in the lemon juice and zest until combined.
Gradually add the flour mixture, beating on low until combined.
Add the oatmeal and beat until combined.
Use a small ice cream scoop, scoop out some dough and place the cookies on the cookie sheet.
Place the 1/3 cup sugar in a small bowl alongside another small bowl filled with water.
Dip the bottom of a flat glass in the water and then in the sugar.
Lightly flatten each cookie.
Bake in the oven for 10 - 12 minutes.
Allow the cookies cool for a few minutes before moving to a wire rack.
Once cooled, dip the top of the cookies into the icing.
Place back on the wire rack and allow icing to harden. Enjoy!