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Cut the dead or diseased stalk back to the base of the plant. Cut damaged stalks below the damaged part to leave the foliage to feed the plant. Prune the stalks back to the base of the plant in late fall when the lilies have stopped blooming and the foliage is dying off. Pruning shears.
True lilies should be trimmed (after blooming) so that 2/3 of the stem is still standing. Then the stalks are cut back to the ground in fall, after all foliage turns brown. But your question is about daylily foliage, and I'm getting off subject.