To begin, preheat the oven to 350. Grease a 9x9 or 8x8 square baking dish or line it with parchment paper.
In a large mixing bowl, mix the milk, lemon juice, sugar, olive oil, vanilla, lemon, baking powder, baking soda, and salt together. Add the flour and mix until a smooth batter is formed. Add the blueberries and fold them in.
Pour the batter into the prepared baking dish. Bake in the oven for 40 minutes or until it is completely cooked through the center.
While the blueberry lemon olive oil cake is baking, use a whisk or fork to prepare the glaze. Simply mix the butter, cream cheese, and powdered sugar together in a small bowl.
Once the blueberry lemon olive oil cake is done baking, allow it to cool and serve it topped with the glaze. Enjoy!