Preheat your oven to 350°F (180°C). Line a 2lb loaf tin with parchment paper.
Grate the zest from 2 lemons.
Cream the butter and sugar together until fluffy.
In another bowl, whisk the eggs, milk, and lemon juice. Gradually mix this into the butter and sugar, ensuring each addition is well combined.
If the mixture appears split, add a bit of flour to smooth it out.
Fold in the dry ingredients and lemon zest until just combined.
Pour the batter into the prepared tin and bake for 50-60 minutes, or until a skewer comes out clean.
For the lemon drizzle, combine the sugar and lemon juice. Once the cake is out of the oven, poke holes in the top and pour the drizzle over while it's still warm.
Let it cool in the tin for a few minutes before transferring to a wire rack.
To make the optional icing, mix the icing sugar with lemon juice or water until you reach your desired consistency. Once the cake is completely cool, drizzle the icing on top.
Notes
Feel free to adjust the amount of lemon juice in the icing to your taste.