Flowers from Daylilies are not toxic and are fine as a treat. If leaves are nibbled occasionally there should be no problem, but do not feed large amounts as reports say that eating leaves of the Daylily in large quantities can cause hallucinations.
On no account should you allow your tortoise to eat the tuberous or fibrous roots of this plant.
N.B. ALL other Lilies are TOXIC so you must make a correct identification before feeding to your tortoise.
Day Lilies are not actually true lilies and are members of a different botanical family.
One way to differentiate the Daylily from other Lilies is that leaves of Daylilies are long and slender, with a central rib on the underside, and the flowers are at the top of smooth, leafless stems.