Preheat oven to 350°. Line bottoms of 3 greased 9-in. round baking pans with parchment; grease parchment.
Cream butter and sugar until light and fluffy. Beat in 1 egg at a time. Gradually beat in molasses. In another bowl, whisk together flour, baking soda, spices and salt; add to creamed mixture alternately with milk. Transfer to prepared pans.
Bake until a toothpick inserted in center comes out clean, 20-25 minutes. Cool in pans 10 minutes before removing to wire racks; remove parchment. Cool completely.
Beat cream cheese, butter and lemon zest until blended; gradually beat in confectioners' sugar. Spread or pipe 2/3 cup frosting between each layer. Top with remaining frosting. If desired, sprinkle with crystallized ginger. Store in refrigerator.