Preheat oven to 170 degrees celsius (fan-forced). Grease and line a 20cm x 20cm cake tin with baking paper. Set aside.
Place the butter, caster sugar and lemon zest into the Thermomix bowl. Insert the butterfly and mix for 30 seconds, Speed 4. Scrape down the sides of the bowl and repeat until smooth and creamy.
Add the eggs and lemon juice and mix for 10 seconds, Speed 4, to combine. Remove the butterfly.
Add the baking powder and flour and mix for 10 seconds, Speed 4. Scrape down the sides and repeat for a further 5 seconds.
Spoon the mixture into the prepared tin and bake for 20-25 minutes or until a skewer inserted into the middle comes out clean.
To prepare the frosting, place the icing sugar, butter and lemon juice into the Thermomix bowl and mix for 20 seconds on Speed 4. Scrape down the sides of the bowl with a spatula. Mix for an extra 30 seconds, Speed 4.
If the frosting is a little too thick, add a bit more lemon juice and whisk again. If too thin, add a little more icing sugar.
Spread the frosting over the cooled slice and allow to set.