I have to add a few words of caution here. There is a report that large quantities of the leaves are hallucinogenic. Blanching the leaves is said to remove this hallucinatory component, but the report does not make clear what it means by blanching, it could be excluding light from the growing shoots or immersing them in boiling water. As far as I know eating the cooked leaves is perfectly all right, it is only the raw leaves that have the effect. You would also need to eat quite a few pounds of the leaves to obtain the effect.
Many species also produce tuberous roots, or fibrous roots with occasional spindle-like swellings.
These roots are also edible - Ive only eaten H. fulva but any of the other species are said to be similar. The roots can be eaten raw or cooked and have a very pleasant nutty flavour that is like a blend of sweetcorn and salsify. Young tubers are the best, though the central portion of older roots can also be used. Dont expect large crops of roots though, this will be just an occasional bonus crop when you are dividing plants. Hemerocallis also have a number of other uses.