Preheat oven to 350℉. Line an 8x4 inch loaf pan with parchment paper.
In a large bowl, whisk together the egg, olive oil, milk, vanilla, lemon zest and lemon juice until combined. Next, whisk in the sugar. Then, add in the flour, baking powder, baking soda, salt and mix until incorporated. Fold in the 1⅔ cups of strawberries. Transfer mixture to the loaf pan and spread out evenly. Top with the remaining 1/3 cup strawberries. Bake for 50 minutes to 1 hour or until a toothpick comes out clean. Check it at the 30 minute mark to make sure the top is not browning too much, if it is tent it loosely with a piece of aluminum foil. Allow to set in the pan for 10 minutes. Transfer to a wire rack to cool completely before icing.
Lemon Icing:
In a small bowl, whisk together the powdered sugar, heavy cream and lemon juice until completely smooth. Drizzle on top of cooled cake.