Rabbits are voracious eaters of the succulent lilies as they grow out of the soil. Is the stem cut at a 45-degree angle? That is the tell-tale sign.
Some gardeners use hot pepper spray in the hope that it will keep the rabbits from eating the plants, but this treatment has had mixed results and has to be repeated after every rain. Try treating some of the lilies, leaving others as a control, and see what happens. Fencing is also a very effective technique to use.
For additional assistance on identifying the culprit, go to Wildlife Damage Identification.