Preheat the oven to 375F. Line a muffin tin with baking cups and set aside.
In a small bowl combine soy milk and apple cider vinegar and let sit for 10 minutes to curdle. In another bowl combine flour, baking powder, baking soda, salt, and poppy seeds. Set aside.
In a large bowl whisk together sugar, oil, vanilla extract, and the lemon juice and zest. Slowly add curdled soy milk, whisking while adding, until completely incorporated. Add the dry ingredients to the wet, folding in gently until just combined.
Fill the muffin liners ⅔ full and bake for 18-20 minutes, until a toothpick inserted in the middle come out clean. Set the muffins on a cooling rack to cool.
While the muffins bake, whisk together the powdered sugar and lemon juice. You may need to add a little extra lemon juice to get a thick and smooth consistency.
Spoon about 1 tablespoon of glaze over each warm muffins then let the muffins continue cooling until completely cool.