Set the oven to 350°F (175°C) and prepare a loaf tin by greasing it or lining it with parchment paper.
In a mixing bowl, combine the flour, baking powder, baking soda, and salt by whisking them together.
In a separate bowl, whisk together the non-dairy milk, sugar, melted vegan butter, lemon juice, lemon zest, and vanilla extract until fully incorporated.
Gradually fold the wet ingredients into the dry mixture, stirring gently until combined.
Transfer the batter to the prepared loaf tin and bake for 45–50 minutes, checking for doneness with a toothpick—it should come out clean.
Stir together the powdered sugar and lemon juice in a bowl until the mixture becomes smooth and shiny.
While the cake is still warm, poke small holes on the top and drizzle the glaze over it to let it soak in.
Allow the cake to cool fully before cutting it into slices and serving.