Make the cupcakes. Preheat oven to 350 F and line a muffin pan with paper liners.
Vigorously beat together sugar, milk and coconut oil until it resembles applesauce. Mix in vanilla, lemon juice and zest.
Sift in about half the flour, all the baking powder, baking soda and salt. Mix until relatively smooth. Add the remaining flour and mix until smooth and no large lumps remain.
Lightly spray the liners with cooking spray and pour batter into liners, filling 3/4 of the way. Bake 16 to 18 minutes, until a toothpick inserted into the center comes out clean. Transfer to a cooling rack and let cool completely.
Make the buttercream: First, puree the strawberries in a food processor. In a large mixing bowl, using an electric mixer, beat the coconut oil and strawberry puree and gradually add the powdered sugar, scraping the bowl as you go. Add the vanilla and mix until smooth and creamy. If it seams loose then place in the refrigerator to set up a bit, then fluff with a fork.
Spread frosting onto cooled cupcakes using the back of a spoon (or your preferred method). Top with a strawberry half!