It may be slugs. They munch the tips off as they first come up out of the ground, and pretty speedily too! Make a perimeter of slug bait around your bed - or around each lily - and that should solve the problem. (If, it's slugs.)

-Helen

My experience has been that it's rabbits that get the emerging growth tips on lilies. I've used Liquid fence - since deer are my biggest problem - with success. Have also read on these forums that the smellier the better cheap carpet deodorizer is also good as a deterrent - especially on and around some of the annuals rabbits like to chew. To be on the safe side, though, after cutting back my lily foliage in the fall, I leave an inch or two of stem above the soil so I know where to look first thing in the spring and use chicken wire cages to protect the clumps I admire most and would be most upset at losing to critters. I know that caging things would ruin a garden for some, but losing your lilies for a whole season ruins things too. And as far as I'm concerned, the chicken wire just blends into the background, hardly notice it.

Curios,
I live in NJ too and was trying to establish lilies in the garden this year. However, I am having the same experience as you. Not slugs, could be rabbits too but chipmunks were caught in the act already by my husband. Plus they are digging holes around the bulbs and taking them out. I suspect its a joint effort with the squirrels as they seem to do similar damage.
There is a cinnamon spray I tried last fall for my camellias. It seemed to deter them - can't say for sure yet.
Here is my recent Brent and Becky order:

Yes, that bulb damage does look like chipmonks - they're looking for water which is why they go for the more succulent things - hens & chicks, sedums, moss roses, bulbs etc. Truth be told, I leave a clear plastic tray of water on my patio along the run for my two resident chipmonks. Since doing that for a couple of seasons now, they have a ready source of water and don't dig. Might not be a universally popular idea, but it's worked for me.

I have a lot of spruce trees and the squirrels seem to go for the cones rather than anything in my gardens - and they also have my neighbor's bird feeder to raid.