In a large mixing bowl, whisk together the lemon pudding mix and milk until smooth and thickened, about 2 minutes.
Gently fold in the whipped topping until fully combined.
In a 9x13-inch baking dish, arrange a layer of graham crackers on the bottom.
Spread half of the lemon pudding mixture over the crackers.
Repeat with another layer of graham crackers and the remaining pudding mixture.
Top with a final layer of graham crackers.
In a small bowl, mix the powdered sugar, lemon juice, vanilla extract, and lemon zest until smooth.
Spread this glaze evenly over the top layer of graham crackers.
Cover the dish with plastic wrap and refrigerate for at least 4 hours or overnight.
Slice into squares and serve chilled.