Preheat oven to 350 °F (176 °C) and line a cupcake pan with paper liners.

Whisk together flour, baking powder, baking soda, and salt in a medium bowl.

In a large bowl, beat butter, oil, sugar, and vanilla on medium-high until light in color and fluffy, about 1½–2 minutes.

Add eggs one at a time, mixing well after each and scraping down bowl as needed.

Add half of the dry mixture and mix until just incorporated. Combine milk and lemon juice and add with lemon zest, mixing until smooth.

Mix in remaining dry ingredients just until batter is smooth; avoid over‑mixing.

Fill liners about ¾ full and bake 15–18 minutes, or until a toothpick comes out clean. Cool completely on wire rack.

For frosting, beat butter until smooth. Add half the powdered sugar and mix. Add vanilla, lemon juice, zest, and a pinch of salt, then beat in remaining sugar until fluffy and spreadable.

Pipe or spread frosting onto cooled cupcakes; garnish with half a lemon slice if desired. Store covered at room temperature up to 24 hours, then refrigerate and serve at room temperature.