Preheat the oven to 350°F/180°C and line 2 half size baking sheets with parchment paper or silicone mats.
In a large bowl, combine strawberry cake mix, eggs, oil, and flour if using. With a spatula, mix together until combined. A few lumps is ok, do not over mix. For thicker cookies, add half a cup of flour. You can add up to 1 cup of flour, depending on the texture you'd like. (see note 1)
Using a medium OXO cookie scoop (1 ½ tbsp size), scoop out cookie dough balls 3 inches apart.
Bake in a preheated oven for 12 minutes, then cool down completely on a wire rack.
To make the glaze, in a bowl combine the powdered sugar with strawberry puree and lemon juice.
When the cookies have cooled down completely, glaze the cookies while they are still on the wire rack, so that the glaze can drip off of the cookies if needed. Leave to set until dry.
Notes
With added flour, these cookies are thick and don't spread quite so much. The recipe will work without added flour, but the cookies will be quite thin. It's up to you what texture you want. In the photos here, I did add ½ cup of extra flour to the cookie dough. You can add up to 1 full cup of additional flour as needed.
To make fresh strawberry puree, simply mash 3-5 strawberries until they are mostly liquid. You can strain out the seeds if you like. Fresh or frozen and thawed berries can be used. Alternately, a low-sugar strawberry jam can be used.
Be sure to allow 3 inches of space around each cookie when baking. These cookies will spread quite a bit.
Don't try to glaze cookies while they're still warm. Allow them to cool completely before making and adding the glaze.
To Store: Keep these cookies in a single layer in an airtight container for 2-3 days. These cookies can be frozen without the glaze for up to 2 months.