Sift together the flour, baking soda, baking powder and spices. Set aside.
In a large bowl, cream together the butter and vegetable shortening. Add the brown sugar and mix until light and fluffy, about 3 minutes. Add the egg and stir well until completely combined. Mix in the molasses, lemon zest and rum. Add the dry ingredients, in parts, and stir until the dough comes together. It should be firm and slightly sticky to the touch. Divide the dough in half and wrap each half, tightly, with plastic wrap forming them into disks. Place in the fridge and allow to chill for at least 3 hours or overnight. It can be made up to three days in advance.
Preheat oven to 350ºF. Working with one dough disk at a time—keeping the second disk in the fridge—roll it out onto a lightly floured work surface. The thicker you roll out the dough, the chewier the cookies will be. And the thinner you roll it out, the crispier they will get. You can decide how to roll it, depending on your taste for gingerbread. Cut into desired shapes and place on baking sheets, lined with parchment paper. Space them out evenly, leaving enough space for spreading. They won't spread too much, but you don't want to crowd them so that they end up baking together. Bake for about 10 to 12 minutes or until the edges begin to brown. Remove the sheets from the oven and allow the cookies to cool for 2 minutes on the pan. Transfer the cookies to wire racks and allow to cool completely. Repeat with the remaining dough.
Whisk together the icing ingredients until completely smooth. If you want a thicker icing, add less water. If your icing is too thin, add a bit more powdered sugar. Pour the icing into a piping bag, fitted with a small round tip, or into a food storage bag with the end cut off. Decorate the cookies as you wish. Allow to set for a few minutes, and then just devour them. Go all in and eat as many as you can. Store any leftovers in an airtight container. What leftover though? Will keep for up to a week at room temperature. Enjoy!