Cake

1. Preheat the oven to 180C/350F
2. Line a 9 x 5 inch / 22 x 13cm loaf tin with baking paper
3. Add sugar, butter, and oil to the bowl of a stand mixer and beat for 5 minutes on medium-high speed, until light and fluffy
4. Add the eggs and vanilla extract to the butter and beat on high for 1 minute, until well combined
5. Combine flour, baking powder, and salt together in a medium-sized bowl, and whisk to combine
6. Add half the flour mix to the butter mix and beat until just combined
7. Add the milk, followed by the rest of the flour and lemon zest, beat until just combined
8. Transfer the batter to the cake tin and bake for 45-50 mins, or until an inserted toothpick emerges clean
9. Set aside as you make the lemon syrup

Lemon Syrup

1. Combine the lemon juice and sugar in a small saucepan or microwave-safe bowl and heat until the sugar has completely dissolved
2. Use a skewer to poke holes all over the surface of the cake
3. Pour the warm lemon syrup over the warm loaf cake
4. Set aside to cool and soak for 30 minutes

Lemon Icing

1. Combine the lemon juice and sugar together in a large bowl, whisk until smooth
2. Add more lemon juice if the icing is too thick, and add more. sugar if it is too runny
3. Drizzle over the cooled cake and set aside for 30 minutes to set