First, make the cupcakes. Preheat oven to 350F and line two muffin pans with 20 muffin liners.
In a small bowl, whisk together the ground flaxseed with the water and set aside to thicken.
In the bowl of a stand mixer, combine the sugar, flour, baking powder, baking soda, salt, lemon zest, and poppyseeds.
Add in the vegan butter, and beat on low until it's incorporated and has a sandy texture.
In a small bowl, whisk together the oil, flaxseed mixture, nondairy yogurt and lemon & vanilla extracts, nondairy milk, and lemon juice. Add them to the dry ingredients. Beat on medium-low until smooth and creamy.
Divide batter evenly among the prepared cupcake liners. Bake cupcakes for 20-25 min until they are fluffy and a toothpick inserted in the center comes out clean.
While the cupcakes cool, prepare the frosting.
In the bowl of a stand mixer, beat the shortening, vegan butter, lemon zest, lemon juice, and lemon extract together until completely smooth and creamy. Add in the powdered sugar, 1 cup at a time, until a thick frosting forms. Add in the salt and some food coloring if desired. You can add a few spoonfuls of nondairy milk if it's too thick.
When the cupcakes are cooled completely, decorate them with the frosting. I used a 1M tip, and decorated the cupcakes with a small piece of lemon slice and extra poppyseeds. Enjoy!