Preheat the oven to 180 C / Gas 4. Grease a loaf tin and lightly dust with flour.
Sift flour, baking powder and salt into a bowl.
In another bowl, beat eggs with sugar until light and fluffy. Stir in vanilla extract and Greek yoghurt. Fold in the flour mixture in 3 to 4 portions using a spatula, then fold in the butter and mix everything till smooth.
Divide the mixture among two bowls. Add the lemon juice and zest to one bowl and the matcha powder to the other. Stir each mixture well to combine.
Pour half of the lemon mixture in the prepared loaf tin, then pour half of the matcha mixture on top. Repeat with the remainder.
Bake in the preheated oven until a skewer in the centre of the cake comes out clean, about 60 minutes.
Let the cake cool in the tin for 20 minutes, then turn out onto a wire rack and let cool completely.