Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking soda, salt, and poppy seeds until well combined.
In a large mixing bowl, cream the softened vegan butter and granulated sugar together until the mixture is light and fluffy, about 3-4 minutes.
Add the lemon juice, lemon zest, almond milk, and vanilla extract to the butter mixture. Mix until fully integrated.
Gradually add the dry ingredients to the wet mixture, stirring gently until just combined. Be careful not to overmix.
Scoop tablespoon-sized portions of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes or until the edges are lightly golden. The centers may look slightly underbaked but will firm up as they cool.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
If desired, prepare the glaze by whisking together powdered sugar and lemon juice until smooth. Drizzle over the cooled cookies for an extra touch of sweetness.