Preheat the oven to 160° C fan.
Line the loaf tin w/ baking parchment.
Mix flour, baking powder & salt.
Grate both lemons & divide the zest. Squeeze the lemon juice.
Whip the eggs & the sugar w/ the electric handheld mixer; add the olive oil & the milk.
Add lemon zest & lemon juice.
Add the flour mix.
Fill the mess in the loaf tin & let it bake for about 40 - 50 min.
After 40 min make the famous test w/ the wooden pin ... & decide if to prolong the oven session by 5 or 10 min or so.
Let the cake rest in the loaf tin for about 10 - 15 min; then lift it onto a cooling rack. Let the cake cool down completely.
Mix the icing sugar, half of the lemon zest, lemon juice & melted butter w/ an egg whip. If too runny add some more icing sugar.
Distribute the sugar mess generously all over the cake & put the cake in the fridge for about 20 min until the icing is fine.