Hi, only snip off the flower head after it fades. When the leaves turn yellow/brown, you can cut it down.

But until they do, keep them fed, since they are building next year's blooms.

when you say lily is it a true lily, Peruvian lily or a day lily? is it in a pot or the ground
certainly cut the flower stem down if it is a day lily Hemerocallis . they have lots of leaves coming from the soil, and are an herbaceous perennial. comes back next year.
If the plant has leaves all down the stem of the flower and they are quite soft/flexible then that could be the Peruvian one [alstromeria] cut the spent flowers off only. they die off and underground with white fleshy storage roots/tubers.

If the plant has leaves all down the stem of the flower and they are quite firm/waxy then it is a true lily. [Lilium] Again just remove the spent flower head. they grow from a bulb.

if in pots then keep giving them a feed to help build them up for next year. if in the ground then I don't tend to feed them.