A good substitute for the cookies are vanilla wafers, such as Nilla Wafers in the US. I learned how to make this in Denmark as an exchange student; my host family would slice up lemons and let them sit in the mix in the refrigerator for awhile, and then remove the lemon slices just before serving.
This is also an excellent recipe for any hot day, and can be made in advance and then kept in the fridge. I'm not sure on how long it can hold up in the refrigerator--it's never lasted more than 24 hours when I've made it; everyone eats it so quickly!