Really hard to answer questions like that without seeing pictures and knowing where you are.
It is surprising. I grow lots of lemon balm and have never seen it bothered by anything. It is usually pretty insect repellent.
Off hand it sounds like some kind of caterpillar/ worm type thing. Have you done a thorough search to find your culprit? Check undersides of leaves, leaf nodes, and the base of the plant. If you don't find it, come back at dusk and again after dark with a flashlight and look some more.
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