I planted lemon grass as an annual but a wise friend told me to cut it back, dig it up, and overwinter it in pots in the house. It's fun to watch it grow almost an inch a day in the kitchen.
There are over 50 different species of lemongrass.
Mine is Cymbopogon citratus (the common herb used in cooking).
Cymbopogon nardus and winterianus are the two main sources of Citronella Oil - like for insect repellents.