Heat the oven to 350°F (180°C). Oil and line the pan (8 x 4 inch; 20 x 10 cm) pan with baking paper.
To a bowl, add in the sugar and soy milk. Whisk until sugar dissolves.
Add oil and lemon juice. Mix well.
Add self-raising flour and lemon zest. Fold gently just until no dry flour remains.
Transfer batter into the pan. Drop pan once on counter to remove air bubbles.
Bake for approximately 40–45 minutes, until toothpick inserted in the middle comes out clean.
Cool in the pan for 15 minutes, then lift onto a rack. Cool completely before icing or the icing will melt.
In the meantime, make the lemon icing by sifting the powdered icing sugar in a bowl.
Add 2-3 tablespoons lemon juice, stirring until smooth. Add more juice 1 tablespoon at a time, only as needed.
Spread icing over the top of loaf. Leave for 30–60 minutes to set before slicing.
For decoration, add lemon zest or very thin lemon pieces just before serving.