Preheat oven to 350F. Very well butter and line with parchment paper a 8" cake pan. Set aside.
In a stand mixer fitted with the whisk attachment, combine the sugar and lemon zest. Mix with your fingers for 1 minute to help release the lemon essence.
Add the eggs and vanilla. Beat 1-2 minutes.
Add the olive oil and lemon juice. Beat until silky ribbons are formed as you mix, about 1 minute.
Add the very softened mascarpone cheese or sour cream to whisk until smooth.
Add the flour, then the baking powder, baking soda, and salt right on top. Mix just until combined and batter is smooth. Fold in the chopped fresh strawberries.
Transfer the batter into the prepared loaf pan.
Bake 15 minutes at 350F, then 25-30 minutes at 325F. It is done baking when a toothpick into the center comes out clean.
Remove from oven. Let the loaf cake cool in the pan for at least 15 minutes prior to removing to a wire rack to cool completely.
Mix all the strawberries glaze ingredients together. Add more powdered sugar or water as needed for a thick, but runny glaze. Evenly drizzle on top of the cooled strawberry cake to enjoy!