In a large bowl, cream together the vegan buttery spread and the granulated sugar. Add the lemon juice, lemon zest, and unsweetened applesauce and mix together on medium low speed.
Add the flour and salt, and mix until combined.
Divide the cookie dough into two even pieces and flatten each portion into a disk. Wrap in plastic wrap and refrigerate for at least two hours.
Preheat oven to 350 degrees, and line two cookie sheets with parchment paper.
Place the dough on a rolling surface covered with flour, and coat the rolling pin with flour, too.
Roll out the dough until it is ¼ inch thick. Cut out desired shapes and place on the cookie sheets.
Bake at 350 degrees for 10-12 minutes.
Prepare the frosting: Cream the vegan buttery spread and add the sifted powdered sugar and the lemon juice a little at a time until the frosting is the thickness that you desire. Depending on the amount of liquid, you can make a spreadable frosting or more of a glaze.
Frost the cooled cookies and sprinkle with decorating sugar.
Store frosted cookies in the refrigerator.