Preheat the oven to 350°F.
Line an 8" x 8" pan with parchment paper or spray it with cooking spray.
In a medium bowl, mix together the wet ingredients until well combined.
In a small bowl, mix together the dry ingredients until well combined.
Add the dry mixture to the wet and mix just until combined.
Pour the batter into the prepared pan.
Bake 17 - 20 minutes or until a toothpick inserted in the middle of the cake comes out clean.
While the gingerbread is cooling, prepare the frosting.
With an electric mixer, beat the cream cheese until fluffy.
Gradually add the powdered sugar and beat until well combined.
Add in 2 tablespoons of lemon juice and taste. If desired, add the remaining 2 tablespoons of lemon juice.
Spoon a dollop of frosting over each piece before serving and top with candied ginger, if desired.
Store the unfrosted cake at room temperature for up to 4 days. If frosted, store it in the refrigerator.