I would wait until the entire stem is brown, too, or at least the entire stem begins to turn brown (after being yellow).
The normal process of lily die back dictates that essentially the entire stalk should turn color at the same time. If your lilies don't do that, it doesn't necessarily mean something is drastically wrong, but there must be one or more reasons why. Perhaps an insect infestation on part of the stem, or mechanical damage, disease, environmental stress, etc.
Remember multiple cuts mean multiple wounds that are vulnerable to infections if you are cutting down to live or dying material. This would include virus transmission via your pruners if you cut one virused lily and then another lily.
