I imagine your cat is merely wanting a bit of salad with its dry or canned main course. Some people say cats and animals, even though mainly meat eaters, do need the nutrients provided in vegetation periodically. Another possibility is the cat is getting a catnip effect from the liriope plant. They roll over, rub their face, extend their claws and twist their bodies when they semell its pungent ordor. The scent probably excites cats because it contains a chemical called trans-neptalactone, which causes the same reaction in cats as a sexual stimulus.
Most seed pods turn from green to yellow then brown when dry.
Sometimes if you wait until they are brown the pods may shatter and seed will be lost. To prevent this wait until the majority of the seed pods are yellow then cut the plant or stems and invert them in a paper grocery bag to dry. Good luck with your seed harvest. I know that it comes from Iran and Afghanistan and is harvested by local people. Dorema ammoniacum, a Persian plant, used in medicine as a cement.