My Day Lilies have bloomed and the foliage is starting to turn brown. Can I cut them back now?

I would leave them go for a while yet. If the brown leaves look untidy, (and I know they do) just pull or trim those off.

Sue's advise is the way to go. I just pull all the Dead leaves out. I have gone as far as using a scissor to cut the brown tops on the leaves. That is extreme if you have a lot. Some people just mow them over. The foliage will grow back before winter.