In the bowl of a stand mixer, weigh out the butter and sugar.
Mix on medium speed with a paddle attachment for about 5 minutes, until very pale and fluffy.
Meanwhile, sift the flour, baking soda, and salt, and set aside.
Using a fine grater, remove the outer zest from two lemons.
Add the zest from both lemons to the butter mixture, along with the juice of one lemon.
Beat until well combined.
Add the eggs to the butter mixture, one at a time, beating well and scraping down the bowl after each addition.
Sprinkle the flour mixture into the mixing bowl, and stir on low speed until just incorporated.
Transfer the cake batter into the prepared loaf tin, and bake for about 1 hour, until the top of the cake is firm.
When the cake is almost ready to come out of the oven, combine the juice of 1 lemon and 100g of caster sugar, and microwave together until the sugar is melted. While the hot cake is still in the tin, pour the drizzle over the top of the cake.
Leave the cake to cool completely before removing from the tin.
If you like, you can decorate the cake with a thick icing made from lemon juice and icing sugar, slices of lemon, or lemon zest.