I've never gardened in a cold climate, or even a cool one, but I can tell you that even in my subtropical climate, lemon verbena is deciduous, and can die right back to the ground in our very mild winters. I chop it back almost to ground level, and it comes back in spring.

You could do the same, but pot it up and bring it indoors as soon as you notice the leaves falling. It's a fairly tough plant.

Alternatively, take a cutting while it's still strong, and plant that out in spring, sacrificing the mother.

Thanks very much for your help! I did think about taking cuttings, and I'll try cutting it back and saving the parent too. I think this is going to become one of my favorites to have every year. I love the flavor! :)