Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.

In a medium bowl, whisk together flour, baking soda, and salt.

In a stand mixer, beat butter and sugar until light and creamy, about 2-3 minutes.

Gradually add lemon zest and lemon juice to the butter-sugar mixture. Mix until combined.

Slowly add the flour mixture to the wet ingredients. Mix until just combined.

Fold in the oatmeal gently until evenly distributed.

Using a cookie scoop, portion out dough onto baking sheets, spacing 2 inches apart.

Dampen the bottom of a glass, dip it in sugar, and flatten each dough ball slightly.

Bake for 10-12 minutes until edges are lightly golden. Cool on baking sheets for 5 minutes, then transfer to a rack.

Mix together confectioner's sugar, lemon juice, and lemon zest to prepare the glaze.

Dip the tops of cooled cookies in the glaze and let excess drip off.