Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x13 inch pan.
In a large bowl, stir together cake mix and vanilla pudding mix. Make a well in the center and pour in eggs, oil water and poppy seeds. Beat on low speed until blended. Scrape bowl, and beat 4 minutes on medium speed. Pour batter into prepared pan.
Bake in the preheated oven for 35 to 40 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool completely. Spread lemon pie filling over the cooled cake.
In a large bowl, mix instant lemon pudding with milk. Mix well and let stand about 5 minutes until fairly set. Fold in thawed whipped topping. Spread over pie filling. Refrigerate for at least 4 hours before serving.