It looks like leaf streak, see:
http://www.daylilies.org/ahs_d...
http://hyg.ipm.illinois.edu/ar...
If so, it's quite common in daylilies, and not always a significant problem. You certainly could check for pests because the leaf streak fungus is believed to need a wound of some kind (weather damage can do it too) to infect the plant. It's not unusual for some daylilies to get "ratty" looking leaves after they've finished flowering.
I'm not certain but in your top picture it looks like there could be leafminer damage, or is it a liquid of some kind that is running down the leaf? For comparison, see:
http://www.daylilies.org/ahs_d...
