This photo shows, better than most photos on the web, how Lemon Verbena grows as a bush when pruned closely. In it's natural environment, which is South America and the Middle East, when left to grow naturally, it becomes a large bush, or a small tree. That is impossible for most of us living in the temperate zones.
We are located in USDA Zone 7b, which is on the edge for Lemon Verbena's annual/perennial status. With protection, and depending on the winter temperatures, a Lemon Verbena plant may overwinter here. But it's iffy, completely unreliable. Temperatures lower than 10 degrees F will generally kill it, but sometimes, surprisingly, it survives.
We don't try to overwinter our Lemon Verbena plants in the field. It's not practical in USDA Zone 7b. We start over in the spring with new plants, for best new growth and reliable harvest of fresh leaves.