What zone do you live in?

Zone 5, central Illinois

It depends on the species of EE, but most common ones can be lifted and stored like bulbs over the winter. Do you know wha t kind you have? Or have a picture of it over the summer?

So, should I pull it out of the pot and store the bulbs/tubers or just leave it as is....

If you can't bring it indoors and leave it in a sunny spot, cut off the green and store the tuber dry and cool.