Preheat oven to 350° F. Line 2 baking sheets with parchment paper and set aside.
In a stand mixer using the paddle attachment, cream together the butter and sugar until it is light a fluffy. Blend in lemon juice, lemon zest and 2 eggs.
In a medium bowl, whisk together the baking soda, baking powder, salt, flax seed, oats, and flour. Then fold in the wet ingredients from the mixer bowl until combined.
Gently fold in 1 cup blueberries. Refrigerate dough for 15 minutes.
For each cookie, roll dough into a medium sized ball and then flatten a little. Place ~1 Tbsp cream cheese in the center of each cookie and form the dough around it. Place each cookie on parchment paper.
Bake ~16 minutes.
While in oven, make glaze by mixing lemon juice and powdered sugar together. Once cookies have cooled for ~5 minutes, drizzle glaze over cookies.
Once you make these, I would recommend enjoying them right away or placing in the fridge. If left in a baggie on the counter there will be too much moisture and they cookies will get soggy. We don't want soggy cookies!