Why don't you get an outdoor kitty litter box. Or a cardboard tray with kitty litter in it that can be disposed of when the time comes. Lime can give a burn to cats or dogs feet it is caustic. As you are doing now I certainly hope you clean up what solid waste there is daily.

You could possibly add some charcoal to the soil

Adding charcoal to your garden soil greatly improves it too for growing plants and vegetables. Glad you mentioned it Badfish.

An outdoor litter tray in the UK would need to be under cover because we get such a lot of rain.
Can you not simply dig the patch over every day or two to bury it?

Surely if you treat the patch with anything it will cause the cat to go elsewhere which will be possibly a disadvantage, its better to know where the cats have been, I have three cats here and they also tend to stick to one area, I turn it over every few days, an outside litter tray is ok if one can have it undercover, unless of course one also has dogs like us, oh the joys of pets and a garden, lol.....

cats are very clean and have a keen sense of smell . especielly there own droppings . lime was dr crippins faverite for melting bodies and the natzies so that leaves the outside litter box realy .