Make cookies: In a medium bowl, whisk together flour, baking soda, ginger, cloves, cinnamon, and salt. In a large bowl, using an electric mixer, beat butter and granulated sugar on medium-high until creamy, 3 minutes. Add egg and beat to combine. Add molasses and beat to combine, scraping down bowl as needed. With mixer on low, gradually add flour mixture and beat until combined. Wrap dough in plastic and refrigerate until firm, 1 hour (or up to 3 days).
Preheat oven to 350 degrees, with racks in upper and lower thirds. On a lightly floured work surface, roll out dough to a 1/4-inch thickness. With a sharp knife or cookie cutter, cut dough into small 2-inch-wide triangles. Arrange triangles, 1 inch apart, on two parchment-lined baking sheets. Bake until cookies are firm and golden at edges, 10 to 12 minutes. Let cool completely on sheets on wire racks.
Make icing: In a small bowl, combine lemon juice and confectioners' sugar and whisk until smooth. Drizzle icing over cooled cookies and sprinkle with sanding sugar, if desired.
Store cookies in airtight containers, up to 1 week.