Preheat your oven to 350°F (180°C). Grease and flour a 9x13 inch baking sheet.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Beat in the eggs one at a time, mixing well after each addition. Stir in the vanilla extract, lemon zest, and lemon juice.
Gradually mix in the dry ingredients, alternating with the buttermilk, starting and ending with the flour. Mix until just combined.
Gently fold in the sliced strawberries, ensuring they are evenly distributed throughout the batter.
Pour the batter into the prepared baking sheet and spread it out evenly. Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.
For the icing, whisk together the powdered sugar and lemon juice in a small bowl. If the icing is too thick, add milk a little at a time until you reach the desired consistency.
Once the cake is completely cooled, drizzle the icing over the top and let it set.
Slice into squares and serve. Enjoy your delightful lemon strawberry sheet cake!