Has the area been extremely wet? I could be wrong but I think the problem is the bulb is starting to rot. The growth point is completely rotten. Bulb rot will spread to other plants. I would cut it back and look at the interior of the plant. If it is brown inside then dispose of the entire plant by digging it out.

I don't see any growth that looks like a virus to me with the pix given. I like the direction taz is taking. Don't know what N AZ is getting for weather, but irrigation may be doing it...

Dan

Ok, I cut the tip of one of the lilies off. The stem is NOT brown inside, but a normal-looking whitish-green. Does this rule out bulb rot?

I also think I found out what those "sprouts" in the pictures are: bulbils. The sprouting leaves are coming from brownish-red things that look like small bulbs (which are coming out of the leaf axils). These are probably what looks like stem rot in the pictures.

I still don't know what is causing some of the leaves to twist. Could this be caused by overcrowding? The lilies that are being affected are getting pretty crowded and I'm planning to divide them later this year.

Are you watering from above or with sprinklers? They could have a fungus. Crowding doesn't allow proper air circulation which will lead to fungus and watering from above would make it even worse.

I water from below, but some water does get onto the leaves. It has also been fairly rainy lately (so I haven't even been watering), but these lilies have had a problem since spring (May and June were really dry). Do you know what the symptoms of a fungus would be, i.e., would there be spots on the leaves, etc.

By the way, thank you for all your help and suggestions!

I clearly see mold on the growth tip in 2 of your pictures but I'm not familiar with these lilies so I'm just guessing for the most part. It's possible this could be due to a drought then the plant pumping fluid to the dead tip.
Remove any dead looking parts and play the waiting game would be my approach to the problem. If any new growth looks moldy or distorted then I would toss the plants that look bad or spray with a fungicide if they have some kind of sentimental value. Thinning would definitely benefit the plants. Sorry I can't help with a definite cause. Maybe someone in the lily forum will help.

If you're interested, I posted three more pictures at the link in my original post.

In the .5 to 1 inch section of the tip I cut off, I counted 15 bulblets. That seems like a lot to me.