Preheat oven to 350°F (180°C). Line two baking sheets with parchment paper.
In large bowl, whisk together coconut oil, maple syrup and vanilla. Stir in flour and salt until soft dough forms. Tip dough onto work surface and shape into a disc. Place between two sheets of parchment paper and roll out to 1/4-in. (5-mm) thickness. Cut dough into 36 rectangles, about 2 x 1/2-in. (5 x 1-cm) each or to desired size of rectangles (or use your favourite cookie cutters).
Place cut-outs onto prepared baking sheets; prick each several times with fork. Sprinkle with coarse sugar if using, and pat lightly onto dough.
Bake 15 to 17 min., or until golden brown. Transfer cookies to wire rack to cool completely.
Make lemon shortbread by stirring 1 tbsp (15 mL) lemon zest into the dough mixture. In a small bowl make a lemon icing by mixing together 1/2 cup (125 mL) icing sugar with 1 tbsp (15 mL) lemon juice. Drizzle over baked cookies.