I don't start many daylilies from seed, but I would prefer something much deeper than a egg carton for starting daylily seeds. They are just too small to allow for much root development on a daylily. You could start them in the egg carton, but I would think you would want to transplant them into something larger really quickly so the roots would not get all bound up. I for sure would not plant either the peat pot or the egg carton with the plant. The peat pots are known for drying out if the lip is left above the soil level, I assume the egg cartons would do the same. Not, saying you can't do it, I am sure you could. I would just prefer starting in a deeper container and letting the plants grow until they were large enough to plant outdoors and without the remains of the container.