Sabrina - Here are 2 links to the AHS about daylily disease and pests that you can refer to if needed. Click on the underlined words to read more about each disease/pest:
Daylily diseases:
http://www.daylilies.org/ahs_d...
Daylily pests:
http://www.daylilies.org/ahs_d...
I also get that on mine and I think it is more aging leaves than anything, but I could be wrong. It could be leaf streak. I just pull them off or cut them off. I've never lost a plant because of it. Being outer leaves, I assume those leaves are weakened or older and don't worry about it. I have most of the other diseases listed on that page because I live in the south (warmer climate) and am an organic gardener. I don't think that daylilies can be watered too much. As long as the roots are getting the water and not the crown of the plant, water should not be a problem.
It could also be a nutrient (fertilizer) deficiency or too much of something. But I personally wouldn't worry about unless more leaves start doing that.