Beat eggs in a bowl with an electric mixer until light yellow, about 30 seconds; add lemon cake mix and beat until completely incorporated. Mix lemon pie filling into cake batter mixture until well-blended. Spread batter out into an 11x17-inch rimmed baking sheet.
Bake in the preheated oven until set, about 20 minutes. Cool completely.
Beat confectioners' sugar, cream cheese, and butter together in a bowl until frosting is smooth; add vanilla and stir. Spread frosting over cooled cake and sprinkle lemon zest over the top.