These are indoors? You wouldn't have naked lady leaves outdoors in Jan here in Ohio. I have only grown naked ladies (aka resurrection lily, surprise lily, magic lily) outdoors in the ground. In the ground the leaves die back and pretty much disappear on their own. Indoors you could take them off once they are all yellow and wilted. Outdoors the leaves appear in spring and are gone by June, then flower stalk comes up in August. That's why it is "surprise lily" -- by the time the flower stalk appears, the plant has been long gone and forgotten. And it is magic because the flower stalk is so fast growing; if you aren't watching carefully it is like suddenly you have a tall stalk with a flower bud where (practically) yesterday there was nothing.
The Amaryllis bulb is one that was forced and bloomed for the holiday and so hasn't had any dormant period yet? Then I would pot it up, but keep it in some kind of cool dry unlit storage for at least six weeks. I don't grow Amaryllis, but here's an article about their life cycle: