Doesn't look like a virus to me, more like damage due to stress. Did you have a late hard frost perhaps.

I'm not sure about the late hard frost because I live in another part of the state during the winter (where it doesn't freeze). I would guess that this is not due to a late freeze, however, because my other lilies of the same variety didn't have any problems and are located just a few feet from these lilies. Is there anything else it could be, beside a freeze or virus?

"Is there anything else it could be, beside a freeze or virus? "

Practically anything which acts as a check to growth can cause buds to abort in this way: poor storage of bought-in bulbs, late planting, temporary drought, sudden changes in temperature, etc. You often see aborted buds on seedlings at first flowering, where last year's expectations exceed this years conditions. Nor can you rule out this being frost damage - even seemingly small differences in exposure can leave one side of a clump damaged whilst the rest is OK. Provided you're sure that whatever happened was only a temporary glitch the only thing to do is wait until next year.

I 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). Someone suggested to me that my bulbs may be rotting, so I cut off the tip of one of the lilies to see if the stem was brown inside. The stem is a normal-looking whitish-green. Once I could see the stem from the bottom is when I could see what I think are bulbils.

Could the twisting leaves and aborted buds be a result of overcrowding? The lilies that are being affected are getting pretty crowded and I'm planning to divide them later this year.

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

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

Yes, I saw that some of the leaves in the first pictures were from bulbils - this quite often accompanies the loss of flower buds, so you'll see bulbils on lilies that don't normally produce them. If you want to use them to get more bulbs of this variety just wait until they come off easily and plant them out somewhere to grow on for a couple of years.

I don't think overcrowding is the cause of your problem, though it will eventually reduce the number of flower buds. Splitting the clumps up on a regular basis is always a good idea.

The twisting of the leaves is all a part of whatever damage caused the buds to abort - something hit the top of the stem as the buds & leaves were developing and distorted them.

Did anyone use Round-up anywhere in the vicinity? I know that sometimes a breeze carrying Round-up drifts over to roses and can distort the subsequent growth for awhile. Possibly the same could happen to lily growth.

Just a thought.

Kate

Is the stem fasciated?? A normal lily stem is round to squarish. The closeness of the leaves suggests fasciation; in that case the stem would be a rectangle when seen end on. Think, cereal box shaped instead of coffee can.
If fasciated, nothing to do but wait until next year. It may come up fine, it may split into two bulbs.
Cause of fasciation?? No one seems certain. Some people think it's frost, some think it's one bulb getting ready to split inot two. no one is sure, that I know of.
If the stem is normal, frost would be my other thought as well

The stem definitely isn't round to squarish. I don't know how to diagnose fasciation, but the stem is flattened like you described, both horizontally and vertically, resulting in something resembling a plus sign (+).

"Weed n' feed" fertilizers often used on lawns contain a weed killer called 2 4 D and it is notorious for off gassing and drifting to damage nearby flowers and plants. It is far worse at this than Round Up.