Certified GKH Gardening Expert
Liatris are winter hardy in zones 5 and above. If this is where you are, they will probably be fine outside.
In colder zones (and possibly in the colder portions of their range, since container plants are more exposed to cold than those in the ground) you will need to dig up the underground corms for storage indoors. Pack them in moistened peat moss and store in a cold but not frozen location, such as the refrigerator or unheated basement.