Preheat the oven to 180°C (350°F).
Line a muffin tin with muffin liners and set aside.
In a bowl, mix the flour, sugar, baking powder and lemon zest. Add the olive oil, vanilla extract, lemon juice and soy milk, then stir until you have a smooth batter.
Pour the batter into the tin, filling each muffin liner about two-thirds full.
Bake for 25 minutes. Test with a toothpick inserted into the middle of a muffin: if it comes out clean, they're ready. If not, bake for a couple more minutes.
Let the muffins cool in the tin for 10 minutes, then transfer them to a wire rack to cool completely.
For the icing, combine the powdered sugar and turmeric powder in a small bowl. Stir in the lemon juice until smooth and sticky. Top each lemon muffin with a teaspoon of icing.