Line a 9x13 inch pan with parchment paper or aluminum foil (to help get cake out after freezing).
Cover pan completely with one layer of graham crackers, breaking the grahams into smaller pieces to fill gaps.
In a large bowl, combine pudding packets, Cool Whip, and milk. Pour half the mixture evenly over the graham crackers.
Add another layer of graham crackers, top with remaining pudding mixture, and one final layer of graham crackers.
In a separate bowl, combine softened butter, milk and lemon juice to make frosting. Start with 1 cup of powdered sugar, mix completely. Continue to add more powdered sugar until the frosting is at the desired consistency.
Spread frosting evenly over the cake. Cover and freeze for at least 4 hours, or overnight.