Yes, you can dry it. Lemon Basil will also give you a nice harvest in a short time. The lemon grass you can over winter though in a cool garage and replant it out the following year, which is how I keep it going. And it easily roots in a glass of water...you can even buy some from a grocery store if it has the root ends and grow your own stock plants.
I would think Lemon Balm (Melissa) would be hardy in your area but don't know for sure..it sure makes it through our roughest winters.
