Preheat your oven to 180°C (350°F). Grease and lightly flour a 30 cm (12-inch) loaf pan to prevent sticking. Melt the butter, either using a double boiler or gently in the microwave. Set aside to cool slightly.
While the oven heats, wash the lemons thoroughly. Finely zest the peel, being careful to avoid the bitter white pith. Then, cut the lemons in half and squeeze out the juice, removing any seeds. Set both the zest and juice aside.
In a large mixing bowl, combine the flour, sugar, and baking powder. Add the eggs one at a time, whisking gently after each addition. Then pour in the melted butter, followed by the lemon zest and juice. Mix until the batter is smooth and well combined.
Pour the batter into the prepared loaf pan and smooth the top. Bake for about 40 minutes, or until a skewer inserted into the center comes out clean.
Once baked, remove the cake from the oven and let it cool for a few minutes. To unmold, carefully invert the pan onto a clean surface. As soon as the cake releases and begins to slide out, gently flip it right side up and place it on a serving dish.