Preheat the oven to 350°F and spray a 1lb loaf tin nonstick spray. We like to cut a long rectangular piece of parchment paper and lay it in the center of the tin with overhang for easy removal when the cake is done. Set aside.
Quickly mix together the dry ingredients, including the sugar, in a large bowl with a hand mixer or in the bowl of a stand mixer.
Add the softened butter and mix on medium speed just until smooth and combined, 1-2 minutes. The mixture will be thick because it's only the butter and dry ingredients (Note 1 Reverse Creaming).
In a separate medium bowl or 2-cup measuring cup, whisk together the wet ingredients including vanilla, eggs, milk, lemon zest, and lemon juice.
With the mixer running on medium speed, slowly pour in the wet ingredients. The moisture and acid will overwhelm the batter and it will likely appear lumpy, this is ok. Continue to mix and it will come together. Finish by mixing oono high for 15-20 seconds until it reaches a smooth consistency. Be careful not to over-mix.
Pour the cake batter into a prepared pan and spread evenly on top. Bake for 55-65 minutes. A toothpick inserted in the middle of the cake should come out with a few moist crumbs. It’s ready when the surface is golden brown and puffed with a deep crack down the center. Tent the cake with foil if the top is looking too brown before the center is cooked.
Remove the gluten-free lemon cake from the oven and allow it to cool for approximately 30 minutes then use the parchment paper to remove it from the pan and finish cooling it on a wire rack.
To make the icing, whisk all of the ingredients together in a small bowl. Place parchment paper under the cake and spoon the lemon icing on top of the cake.