Preheat oven to 350 degrees F (175 degrees C). Line baking sheets with parchment paper.
Beat 1 1/2 cups sugar and butter together until light and fluffy. Add egg and vanilla extract and beat until smooth. Beat candied ginger, grated ginger, lemon zest, ground ginger, and cinnamon into butter mixture; stir in molasses.
Fold flour and baking soda into ginger-butter mixture until a stiff dough forms. Roll dough into 1-inch balls.
Pour remaining 1/2 cup sugar into a shallow bowl. Roll dough balls in the sugar and place balls 2 inches apart on prepared baking sheets.
Bake in the preheated oven until cookies flatten, lose their sheen, and slightly crack, about 12 minutes. Cool for 3 to 5 minutes on the baking sheets before transferring to wire racks to cool completely.