It's some kind of borer, Papaipema nebris is one that is said to attack Lilium (it's a moth caterpillar). If you're seeing the white stuff (frass) increase then it's likely still in the stem feeding and I expect the top of the lily may wilt. Not sure but that may not be the only borer that can attack lilies. We'd need to see the culprit to ID it.
