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 2/3 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 tbsp of glaze over each warm muffins then let the muffins continue cooling until completely cool.
Serving and Storing - Serve these muffins immediately with a matcha latte or chai tea. Store leftover muffins in an airtight container at room temperature for up to 5 days. You can also freeze these muffins for up to 2 months. To thaw, pull the muffins from the freezer and let them thaw at room temperature for several hours.
The most accurate way to measure flour is to spoon it into your measuring cup, leveling it off with the back of a knife.
Let the muffins sit in the muffin tin for 10 minutes before flipping them out to a wire cooling rack. Otherwise, the muffins may fall apart.
Glaze the muffins while they are still warm. This allows the glaze to melt over the lemon poppy seed muffins.
If you want to make this muffin batter in advance, store the batter in an airtight container in the refrigerator for up to 48 hours. To bake the muffins, preheat the oven and bake according to the instructions. Muffins may take a few minutes longer to bake since the batter will be chilled.