Prepare the cake according to the package instructions in two 8-inch pans. Allow to cool completely before slicing each layer of cake in half crossways to create 4 equal layers.
In a large bowl, use a mixer to beat the cream cheese until smooth. Add the lemon curd and beat until smooth. Add the whipped topping and mix until well combined. Add the lemon juice and mix completely.
Place the bottom layer of one cake on a serving platter or cake stand and spread about 1/4 of the lemon filling evenly over it. Repeat with the other layers and filling and top the cake with the remaining 1/4 of the filling. If you find the filling too runny, refrigerate it until spreading consistency. Chill the cake completely before serving and store in the refrigerator.