Do not cut the foliage if it is still green. It feeds the bulb for the next season blooming. This is true for all bulbs. If it is already yellow/brown, you can cut it as close to the ground as you want.
You can also ask how to care about your Daylilies (Hemerocallis) on Daylily forum.

Does that mean that when I cut lilies to bring inside and put in vases that I am damaging the plants? yikes.

Yes, you make them weaker by doing this. The bulb will not die, but might not bloom for you next year. Or flowers will be smaller.
Undeveloped seedpods should be removed after flowering if seeds are not desired. This also helps the bulbs to store as much food as possible.

Whenever I cut lilies to bring in, I leave about 2/3rds, if not more, of the stem intact - that seems to work fine, as I have been cutting the same bunch of lilies for a couple years.

Cutting lilies for vases, etc. does not weaken the bulb for the following year. By blooming, it's accomplished what it's supposed to do and by cutting the blooms you're really only preventing the lily from producing seed. Now, cutting down too much of the green stem would impact the bulb. This is not the prettiest time of year for lilies - my foliage is just short of starting to yellow and the temptation is always there to cut them down. But don't do it, you really would be robbing the bulb of what it needs to replenish itself for next season.

I've got some Lilium Tigrinum in a bad spot where deer crop the tops off of just about every year if I'm not quick enough with the Liquid Fence. Despite being cropped in their growing stage or just as buds are forming, those lilies keep coming back bigger than before.