Are they beinding towards the light ?
Have you moved them into a warm room from a cool room ?

You can check the stems for signs of insects.

Is the pot moderately dry ? After they grow and bud, all of a sudden the lilies consume much more water than usual. This means watering more frequently. The color of the soil may still appear "wet" but the roots are in reality short of moisture. Try to water the pot really well for a few minutes so water drains freely out of the bottom of the pot. Then water again when the top of the soil is drying slightly. Everytime, you must ensure good drainage, and water should flow freely. It is not enough to water the top of the soil. Water so water drains and then empty the saucer.

If you can, move the lilies to partial shade for a few days and to a cooler area, if it is very hot where they are.

The symptoms you describe, if not caused by insects eating notches in the stem, is usually from dry potting mix/soil, too hot temperatures (full unrestricted sun during midday or early afternoon), or a sunny window which can get very hot. Even if the lilies have plenty of water, they may still droop if they get too hot.

Check water, temperature, sun exposure, and insect signs.
Too dark areas will cause the lily to bend towards light.

Thank you for your help! I discovered little fuzzy white insects (aphids?) at the branching points and am treating the plants with 2% soap solution daily. I think they are getting plenty of water, and plenty of sunlight. I have them under cedar mulch to help with the heat, which hasn't been too strong so far. The plants that are pest-free are not drooping.

Is there anything I can do by way of nutrition or other care to support the plants' recovery? A friend suggested I wire the tips up straight, is this a good idea?

It is worth a try.. could the white fuzzy bugs be mealy bugs ?? that would explain the stress on the lilies as the eat the sap out of the stems. Why not switch to an insecticide instead of soap water...

{{gwi:2102002}}

Go to a good garden center and look at the lables (back side) of the insecticide bottles. If you find Mealy bugs, then that is a good choice.