Set up grill for indirect cooking over medium heat. (No heat source under cookies). Spray 9 by 13-inch foil pan with cooking spray and set aside.
For lemon layer:
In a large mixing bowl, beat with an electric mixer on low speed the cake mix, butter, and egg until well combined and smooth. Press cake mixture evenly into prepared pan; set aside.
For top layer:
In a medium mixing bowl, beat cream cheese, sugar, and lemon or lime gelatin on medium speed until creamy. Add eggs and beat until smooth.
Spread cream cheese mixture over cake layer. Place foil pan in a second foil pan for stability and insulation. Place on hot grill away from heat. Cover and bake 40 to 50 minutes. Rotate pan halfway through baking. Remove from grill and cool completely before cutting into squares.
Preheat oven to 350 degrees F.
Spray 9 by 13-inch baking pan lightly with cooking spray; set aside. Prepare cake layers as directed above. Bake for 40 to 45 minutes or until cake barely start to pull away from sides. Cool completely before cutting into squares.