Best not to cut them down, but to let them die naturally so this gives the lily what it needs for blooms next year.

Oh, no! I have already cut down a number of them. Hope I haven't done a lot of damage. Guess what's done is done. There are some flowers yet, but I cut down a number of stalks. We are trying to sell our house so I was trying to make things look neat, plus I thought it would help the plant not put energy into things it needed for vigor for the next year.