What kind of lilies are they? I probably can't be of much help to you on this one, as I've never grown lilies in a container, only directly in the ground.
Things I would investigate would be:
1) Does the pot have proper drainage?
2) Does the soil drain rapidly?
3) Is the light exposure correct?
4) Is there any evidence of insects or disease?
Here are a couple of Extension Service articles about potted lilies:
1) How strong was the dilution of soap and water? I usually use 1 tsp (5 mL) to 1 quart (just under 1 L) for insect spray.
2) Was it actually liquid SOAP, or was it a DETERGENT? If it was detergent, go rinse rinse rinse those lilies, leaf stem and root, with as much water as you can. The detergent will burn them and they'll also develop blotches. If the spray was strong enough, they may die.
Sorry, but fast action is the only kind (IF this is the problem) that will work.