Heat oven to 375 degrees F. Place paper baking cup in each of 18 regular size muffin cups.
In large bowl, beat granulated sugar, butter, molasses, and eggs with electric mixer on medium speed, or mix with spoon. Stir in flour, baking soda, salt, ginger, 1/2 tsp cinnamon, the allspice and water. Spoon about 1/4 C batter into each muffin cup.
Bake 15 to 18 minutes or until toothpick inserted in center comes out clean. Cool 5 minutes; remove from pans to cooling racks. Cool completely, about 20 minutes.
Beat cream cheese, 1/4 C butter, the lemon peel, 1 tsp cinnamon and the vanilla with electric mixer on low speed until smooth. Gradually beat in powdered sugar, 1 cup at a time, on low speed until smooth. Beat in milk 1 tsp at a time, until spreadable.
Pipe or spread a generous amount of frosting on top of each cupcake. Store covered in refrigerator.