Preheat oven to 400 degrees F and grease a 11×17″ sheet pan with non stick spray.
In a large bowl, stir together butter and sugar with a whisk. Add eggs one at a time and whisk until smooth.
Add milk, baking soda and vanilla and whisk until combined.
Zest and juice 2 lemons.
Stir in flour and lemon zest. Add hot water and only ¼ cup of the lemon juice and stir slowly until combined.
Spread into prepared baking sheet and bake for 15-18 minutes. Remove from the oven and cool to room temperature.
In a medium bowl, combine sugar, butter, 2 tablespoons lemon juice and vanilla and whisk until combined. Add additional lemon juice to thin further if desired. Spread over cooled cake and let set before slicing.
