Preheat the oven to 180°C, fan 160°C, gas 4. Grease and base-line a 900g loaf tin.
Place 50g Californian walnuts in a food processor and blitz to a coarse powder.
Beat the 125g butter and the sugar in a large bowl until pale and fluffy. Whisk in the finely grated zest of both lemons, then whisk in the eggs, one at a time.
Fold in the flour, baking powder and ground Californian walnuts to give a smooth batter. Fold in 25g Californian walnut pieces, reserving the remaining 25g for the top, then spoon into the prepared tin and bake for 35-45 minutes until golden and a skewer inserted into the centre comes out clean.
Just before the cake comes out of the oven, mix the juice of 1 lemon with the granulated sugar. Stir the remaining 25g Californian walnuts into the lemon syrup. Prick the cake with a skewer several times when it comes out of the oven and drizzle over the lemon and Californian walnut syrup.
Allow to cool a little in the tin before removing, then allow to cool completely before slicing to serve.