I don't know the answer but your pic reminds me of what my GRAPEADE foliage looks like. Starts out green from the middle and then turns to this variegated coloration as it grows to the outside. No pests and none of the other plants near it show the same discoloration.
If it were a fungus or pest other plants near this one would show perhaps similar signs.

Julia

I've been told it is thrip damage ... and to try insectisidal (sp?) soap in the spring. But I don't know that for sure, and I haven't tried the soap ...

I don't think I've seen anything here resembling your foliage. The mottling does remind me of virus symptoms. The only possibility that comes to mind is mite damage, but that is usually concentrated at one location on the leaf. If you have a 50X magnifying glass, you can usually see them on the underside of the leaf. If you don't see any evidence of insect damage causing this pattern, I would give serious consideration to destroying the plant.
Ed

If you are an AHS member, you should send a few pictures to Sue Bergeron, who could probably give you an answer.She is an expert with this sort of thing. Although CATHERINE WOODBURY has notoriously bad foliage ( and it left here years ago for that reason) I don't recall anything looking quite that weird. The mottled looking foliage does remind me of a virus that I've only seen on hosta.

I'm leaning strongly towards destroying the plant. I do have hostas and am aware of the contagious virus they can have. I guess that's what drew my attention to this foliage.
There is a peony several feet away that has some foliage mottling also, but I'm not sure which one exhibited the problem first.
I've seen thrip damage on my asiatic lilies and it doesn't look anything like this.

I think I'll let it finish blooming and then dig it and the peony out. Thanks for your opinions.

I wish hosta virus was the answer for mine but we don't grow any hostas. Sue B. couldn't identify the problem and several people who responded to my posting on the Email Robin (AHS)several months ago have seen the same thing on their GRAPEADE foliage and just ignore it.
Next year, if the foliage looks the same, I plan to take a sample to Cornell and have them look at what the issue is.

Perhaps I shouldn't say anything, because I can't see the picture (computer at work has blocked it). However, I was reading up on "Rust" because I just bought a few daylilies that had streaky foliage, and I think that I have "leaf streak", which requires
"At the very least, remove dead
leaves with brown spots and streaks in the fall. DonÂt
let these overwinter and provide inoculum for spring
infections. Avoid overhead irrigation, which helps
spread the spores. The third step is to use fungicide
options if necessary. Compass is a product by Bayer
that is registered for use on daylily for this disease. It
contains trifloxystrobin and is a local penetrant, which
means it is locally systemic and has limited movement
in the plant. Thiophanate-methyl has a general
ornamental label and has been shown to be effective
at preventing infection by the leaf streak fungus."
Thought I'd mention it in case you decide this might be what you have.

Cut the foilage, Its not rust, way to uniform for that. I dont know what it is either, but your winter is coming, if its only insect damage or some sort, that will take care of it. I would wait until next years growth before making a decision on it.

I just searched at random for some common daylily rust and leaf streak, I found this page. Your foilage doesnt look like mites, leaf streak or rust.

RUST

I think its kinda neat looking actually LOL... If it was a genetic variation in the foilage, I would keep it!

I don't have a clue about what it is, but I found this page referencing Tobacco Ringspot Virus on the AHS website with a picture that is similar to yours. You might want to compare.

Vickie

Here is a link that might be useful: AHS Daylily Dictionary