01 - Preheat oven to 350°F. Line two baking sheets with parchment paper.
02 - In a medium mixing bowl, whisk together all-purpose flour, baking soda, and salt.
03 - In a large bowl, cream the softened butter, vegetable oil, and granulated sugar with an electric mixer until light and fluffy.
04 - Beat in eggs one at a time, mixing thoroughly after each addition. Stir in lemon zest, lemon juice, and vanilla extract.
05 - Gradually add the flour mixture to the wet mixture, mixing just until combined.
06 - Gently fold diced fresh strawberries into the dough.
07 - Using a tablespoon or cookie scoop, drop mound-shaped portions of dough onto the prepared baking sheets, spacing 2 inches apart.
08 - Bake for 10 to 12 minutes, or until the edges are lightly golden.
09 - Allow baked cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
10 - In a small bowl, whisk together powdered sugar, lemon juice, lemon zest, and crushed freeze-dried strawberries (if using) until a smooth glaze forms.
11 - Drizzle prepared glaze evenly over cooled cookies. Allow glaze to set before serving.