My father always lifted his and after trimming tops, drying and cleaning soil of put them in dry loam (peat then) in boxes, then stored them in garage till spring
I'm not a great gardener in fact I'm pretty lazy and I just leave them in the ground.They keep coming back and the only time I touch them is every 2-3 years when I split and replant them.I live in North Notts and the soil type is a fairly heavy clay.
You can lift and store in a cool, dry, frost free place. They can be left in the ground to take their chances....cut them to ground level and then put at least 6" of mulch over them. This can be straw, leaves, wood chip, compost....as long as it's thick enough to stop the frost getting down to the roots.
Another plus for lifting and storing is that you can divide tubers in spring once shoots are showing and multiply the number you have, or give to friends
It really does depend on where you live. If frost is likely to get deep enough under the soil it will kill them. I lived in the North, in a frost pocket, and lifted them - then stuck them in a box under the bed!