Sounds like a good plan. You'll have plenty lots to play with!
But I don't think the egg carton will decompose fast enough to be planting the individual cups, if that is your intention. Stark layers in the soil profile is never a good thing, and it would hinder the growth. If it were me, I would remove the lilies entirely from the carton. Yes, there will be more transplant trauma, but in the end it will be better.
