Cymbopogon, also known as lemongrass, barbed wire grass, silky heads, Cochin grass, Malabar grass, oily heads or fever grass, is a genus of Asian, African, Australian, and tropical island plants in the grass family.
Keep soil barely moist, as plants grow very slowly over winter. Another option is to store a pot of lemongrass, cut down, in a cool, dark place like a basement. Water just a few times over winter to keep roots alive. In spring, bring the pot into a bright spot, and resume normal watering.