Melt the butter over low heat in a medium saucepan, stirring gently until completely smooth and melted, about 3-5 minutes.

Add the dry lemon pudding mix and 1/2 cup of milk to the melted butter, stirring over low heat for about 4 to 5 minutes until smooth.

Gradually sift in 2 cups of powdered sugar, mixing thoroughly until fully incorporated.

If the mixture is too thick, add additional milk slowly until you reach a smooth texture.

Line an 8x8 inch square baking pan with parchment paper and press into corners.

Pour the fudge mixture into the prepared pan and spread evenly with a spatula.

Chill in the refrigerator for 2-3 hours, or until firm.

Once set, lift the fudge out using the parchment paper and cut into squares.