Well here's prior art which I make on a regular basis.
500g caster sugar
250ml fresh lemon juice (that's about 6 large lemons)
Zest if you like more lemony goodness
Dissolve the sugar in 750ml water and simmer for a couple of minutes. Remove from the heat and add the lemon zest. Allow to cool.
Add the lemon juice. Put in the fridge until really cold.
Place the mixture in an icecream maker and churn until it starts to solidify. If you don't have a machine place in a shallow dish and freeze for an hour. Give it a good forking (fnarrr) to mix the ice with the unfrozen goop. Freeze again for another hour, repeat a couple more times until it is completely slushy. Whisk vigorously then freeze. It'll keep for up to a week in the freezer.
I suspect the cure for cystic fibrosis is somewhat more complex.