It appears that many people had serious problems with botrytis on their lilies this year, especially Asiatic lilies. Could that be the problem?

Thanks for the info, I looked it up. It could also be basal rot, apparently, because they specifically mention stunted growth. I am really worried, I have a ton of these all over and they are the highlights of my garden!

You cannot confuse bortrytis on leaves with other things. The distortion can be also caused by late frost , which damaged the shoot without killing it. If you are worried about basal rot, then try to dig one up and see whether IT IS BASAL ROT. No point in going around and worrying. If it is basal rot, you can at least save some scales which are not infected and try to propagate them .

I have some stunted this year too. I think it was just the crazy weather in April with no rain and many frosts with the cool weather. Some don't have the bud count they usually do.
On the other hand some seem to have divided like crazy over the winter. I have seen that before in a mild winter like we had this year both with lilies and tulips.
BTW what are you spraying them with for red lily beetles?