I bring mine in the house, in their pots, into a sunny room, cut back a bit, and keep it watered through the winter. They continue to grow, etc., and once it is warm I take the pots out to the yard where they leaf out again. Can't imaging it working like dahlia tubers - nothing similar about it.

I bring mine in and overwinter with all my potted indoor plants. I have to battle the aphids but it hangs on long enough to take it outside for the next growing season.

Take your thumbnail and scrape against the bark/stem. If there is still green there it will probably grow out again, if it is dry and crispy I would go lemon verbena shopping. I am in in zone 6, where I have had the base overwinter in mild winters against the house but most years it is killed outside. My wife's aunt in a tropical country has had it grow into almost a small tree form. I usually try to overwinter some in pots. If you grow it potted that should be fine on a sunny windowsill or a cool garage. If the plant is too big you can try to take some nice young cuttings from the growing tips towards the end of summer. They usually root fairly easily.