Preheat the oven to 180C/350F/Gas 4. Line the bottom of an 9x5" loaf pan with baking paper, and grease the sides. Set aside.
Whisk together the flour, sugar, baking powder, baking soda, and salt
Whisk together the egg, lemon juice, buttermilk, and oil. Pour the wet ingredients into the dry ingredients, and mix until just combined. Fold in the lemon zest and chocolate chips. Do not over-mix.
Pour the batter into the prepared pan, and bake for 50 - 60 minutes, or until a toothpick inserted into the centre comes out clean. Cover loosely with aluminium foil halfway through baking to prevent the bread from browning too much.
For the Lemon Syrup
Microwave the lemon juice and sugar together, stirring every 30 seconds until the sugar has dissolved. Brush the syrup over the warm bread, and leave to cool completely in the pan on a wire rack.
For the Icing
Whisk together the icing sugar, lemon juice, and heavy cream. Add more icing sugar if too runny, or more heavy cream if too thick. The icing should be fairly thick, but pourable. Remove the bread from the pan, drizzle the icing on top, and serve.
Notes
This bread stays fresh covered at room temperature for up to 3 days, or in the fridge for up to 7 days. It also freezes well for up to 3 months. Thaw overnight in the fridge.