They might. What "lime and water" mixture specifically are you talking about? Key Lime pie, for example, definitely contains sugar.
Sugar.
The tartness of lemon and the sweetness of sugar combine to make lemonade delicious.
You could place the sugar-clay mixture in a wire-mesh sieve, and rinse the mixture with water to dissolve the sugar and remove it from the clay. You would need to do this over a container that would collect the sugar water. Once the sugar is completely dissolved, you could evaporate the water from the sugar water, leaving the sugar behind. The clay would be left behind in the sieve.
Try adding a little sugar to take the tartness away.
Yes, it is a mixture.
Sugar water is a true solution.
A mixture because the sugar is mixed in the water
cake
Add water, and the sugar will dissolve leaving the sand as a solid. Filter that mixture and the sand will stay on the filter paper and the water and sugar will pass through. Evaporate the water, and you'll be left with sugar only.
Sugar is a chemical compound.
Sugar dissolved in H2O is a mixture
Mixture.