I have been looking around and I have not seen to why lilies are toxic to cats. I know the whole plant is toxic, but why? Just curious.
The webmind says "What makes lilies poisonous is still unknown, but it is known that the toxin is soluble in water and deadly. Cats suffer from kidney failure after ingesting even tiny amounts of this plant and flower." Other organs may also be damaged.
Bodies are basically lazy. Producing enzymes to detoxify everything they might encounter is metabolically expensive, so carnivores often lack some of the paths that deal with phytotoxins. Exactly which ones get optimized away depends on species. Cats can handle caffeine and thiobromine better than dogs do, pound for pound.
As Keshlam noted, the effect of some forms of lilies on the kidneys of cats is well known, but the reason for the toxicity is not.
However, there are also many plants called lily and the toxicity can be different or non-existent, depending on the plant. This is further made difficult because of hybrids.
In the case of lily of the valley, for example, the risk is around the fact that it's a cardiac glycoside which, in more general terms, is a class of drug that modifies the contraction capabilities of the heart muscle (increasing it). Overdosing on this could result in severe poisoning and death and not just in cats, which is why the general drug class is managed quite carefully in medicine.
So, in general, if there is the word "lily" in the name and you have cats, probably best to get it out of reach or, even better, out of the home.