The yellow bottom leaves are typical of clumps of daylilies. As the plant gets larger the older bottom leaves are shaded by the upper growth. I would be more concerned if the upper leaves turned yellow. Most likely the leaf damage is caused by a slug. Monitoring the plant and removing the mollusk helps. Look for daytime hiding places, under a pot or similar refuge from the sun. If the chewing continues, slugs like beer. A saucer of beer will attract them and the inebriated slugs around.
The Asiatic lilies are suseptible to red lily beetle. They are awful! Will kill a plant in no time. The mature beetles are bright red, the larvae are drab ?brown & coat themselves in their own manure (pretty disgusting). I sure hope you don't have lily beetles!
While I do not have an Asiatic lily, the pictured plant growth looks to be new enough to still be light green. Where I would be concerned is if the leaves turned from the darker green to light green. Then you would have a serious problem. Have the leaves changed? Is this the first year you have had these plants? Jerry
I have had good luck making a ring of aluminum foil around a plant. I have also had good luck with DE (diatomaceous earth), although the DE has to be renewed after a rain.
Tina--I think I read somewhere that a ring of copper can be a good deterrent for slugs--something about it giving them a slight electrical shock. I didn't use copper as it was too expensive, so substituted aluminum. It is not as conductive, but did seem to work. Just make a ring around the plant, burying the aluminum slightly in the soil. Think of it being a barrier & you'll get the idea.