First step is to id your bug.
Google Red Lily Beetle and see if that is it. If so, some people handpick them some have had luck spraying with Neem oil.

I just spray mine with regular pesticide, and I guess that protects them until they make more new growth, and it also looks like they gain resistance after the growth hardens off.

Red lily beetles are very easy to spot so when I see them, 1 spray will kill them off pretty easily. Don't let them eat because if they eat, they'll lay eggs very fast, and those turn into more beetles after a couple weeks.

Here is a link that might be useful: my lilies

Help! Something weird is eating my lilies. It looks like spattered mud on and under the leaves. A worm emerges from this blob and eats the leaves. What is it and how can I get rid of it?

most likely the afore-mentioned Red Lily Beetle -- the scourge of true lilies (and fritillaria). the "mud" is the lovely glob of excrement ftom the larvae, which is under the leaves or at the joint of leaf and stem, and in which they protect themselves. i loathe having to squish this mess, so i use Bayer Rose and Garden spray -- blue bottle -- which is a systemic and also kills on contact. it is the BEST stuff, tho don't spray in windy weather or when beneficial insects are flying around. go read the FAQs on this forum for more info. and good luck!