Preheat oven to 170 degrees celcius (fan-forced). Line a muffin tray with cupcake liners.
Sift the plain flour and baking powder into a bowl. Add the sea salt and set aside.
Using a stand mixer or handheld beaters, cream the butter and sugar together on low until combined. Increase speed to high and beat until light and fluffy.
Add the eggs one at a time, with the beaters turning on low speed. Mix until just combined.
Add in the milk, vanilla extract, lemon juice and lemon zest. Mix for 30 seconds on low speed.
With the beaters still on, slowly add the dry ingredients and mix until just combined.
Divide batter evenly among the cupcake liners in the muffin tray.
Bake in the preheated oven for 18-20 minutes or until the top springs back when lightly touched (don't overcook).
Leave the cupcakes in the muffin tray for 5 minutes and then transfer to a wire rack to cool completely.
To make the frosting, place the butter into a large bowl and beat until light and creamy (about 2 minutes).
Slowly add in the icing sugar, lemon juice, cream, lemon zest and salt while continuing to beat the frosting. Beat for a further 3 minutes.
Pipe or spread the frosting onto the top of the cupcakes.