In a small bowl mix together oil, sugar and egg. Beat until fluffy. Stir in molasses, lemon zest and lemon oil.. Set aside.
In large bowl sift together flour, salt, baking soda, cinnamon and ginger. Stir wet ingredients into dry ingredients until combined. Cover with plastic wrap and refrigerate for 8 hours or overnight.
Preheat oven to 350 degrees. Line a baking sheet with parchment paper.
Remove dough from refrigerator. Roll dough into 1 1/2 - 2 inch size balls depending on how big you want sandwiches. Roll the ball into a small bowl of granulated sugar. Place balls on parchment lined baking sheet about 3 inches apart. (cookies will spread so definitely space them out) Bake for 8-10 minutes until edges are set and tops are crackled. Cool on baking sheet for 1 minute then transfer to wire racks to cool completely.
In a large bowl, cream the butter and the confectioner's sugar with a rubber spatula until pale in color. Add the vanilla and continue to cream until light and fluffy.
Assembling the cookies:
When cookies are done cooling, sandwich together with about 1 1/2 - 2 Tbsp. buttercream.