Thanks for writing. I'd guess there are two possibilities: Slugs and lily leaf beetles.
Slugs are slimy creatures that basically look like snails without a shell. They usually feed only at night or during wet, humid weather and often leave a trail of slime behind them. During the day, these trails often appear shiny in the sun. Stop slugs with a slug-and-snail bait, available at your local garden center.
The other option is lily leaf beetle, a bright red beetle that eats lily foliage. The larvae, though, look like slugs, and feed for up to three weeks on the plants' foliage. They drop into the soil and pupate become emerging as the red beetles. One of the safest ways of treating this pest is to physically remove it and squish it or drop it into a bucket of soapy water. You can also spray them with a natural insecticide, such as neem oil (look for it at your local garden center).
---Justin, Senior Garden Editor, BHG.com