It will live. Make sure it has water and sunlight, and it will grow back just like your lawn grass does after being mowed. Of course, it doesn't stand freezing, so can't leave it out when it starts getting cold.

My lemongrass usually thrives for a year or less. When they decline in health, I simply go back to a Vietnamese grocery store and buy more stalks in the produce selection. I select ones that are fresh and have healthy base tissue. After only a few days in water, the lemongrass forms roots. I pot them in soil a couple of months later.

My lemongrass is 2 years old now. I grow it indoors in front of the south-facing patio door all winter, then plant it out in the spring when night-time temps are over 50.

Night time temps here are getting into the mid-40s here now but daytime temps are still up into the 80s, so I've been leaving it out so far. Probably this weekend I will dig it all up, break off a clump and pot it up, and cook with the rest.

Lemongrass freezes easily and well, I clean it off, clip off about half the greens, and freeze it all (including the clipped greens which can be used to make a tisane or for flavoring soups).

I'll put the pot out during the day and bring it in at night as long as daytime temps are warm.

This is the cultivar that won't set seed. The only way to start it is from a piece you get at an Asian market. The bulb should be intact. Cut off all but about the top 4" to 5" of the leaves and root it in a glass of water, then transplant to soil or a potting mix. You can tell which variety it is because the one that sets seed is thinner, like a pencil, while this variety (which I think is the better of the two) has fatter stems, about as thick as your finger.

I use a lot of lemon baum in my tea... can I leave it out all winter?

Lemon Balm is not the same as Lemon Grass. It is totally hardy but it is a herbaceous perennial so it will die down in winter and re-emerge in the spring. If you want to make tea in the winter you'll need to dry some.