Preheat your oven to 350°F (175°C) and grease a 9-inch round cake pan or line it with parchment paper.
In a large mixing bowl, whisk together the flour, sugar, poppy seeds, lemon zest, baking powder, baking soda, and salt until well combined.
In a separate bowl, combine the almond milk, lemon juice, vegetable oil, applesauce, and vanilla extract. Mix until smooth.
Pour the wet ingredients into the dry ingredients and gently fold them together until just combined. Be careful not to overmix; a few lumps are okay.
Transfer the batter into the prepared cake pan and spread it evenly. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Once baked, remove the cake from the oven and allow it to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.
While the cake is cooling, prepare the glaze by mixing powdered sugar with lemon juice in a small bowl. Adjust the consistency by adding more lemon juice if necessary.
Once the cake is cooled, drizzle the glaze over the top. Allow it to set for a few minutes before slicing and serving.