They do not thrive in cold weather. Bellie

If you put it in a pot, you might try a deep one. I put my lemon grass in a 4" deep pot & kept it outdoors all winter one year & it did survive, but did not look great. I was able to bring it back, however, by putting it in the ground in the spring. My outdoor winter lows are 40 degrees usually; rarely freezing, which might mimic a basement in your zone.

It'd be less headaches if you just start a new one every spring. Lemon grass is one of the easiest plants to grow. Dig some stalks up, cut off the long leaf and let them dry in room temp. 1 month before the last frost you can start indoor by stick the stalks in a cup of water. Within a week you will see the roots appear. I usually wait 4 weeks before planting them in the ground. (I have not let them dry for more than 2 months so I'm not sure if they will root.) If not you can always buy the stalks at any Asian market and root them the same way. They are not expensive, 5 stalks for $1. TT