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Yes, you can cut back any dead/brown growth just to where the new growth is beginning to come in.

We do not sell plants. We only offer information in regards to growing them. I would recommend a local nursery in your country, or online nurseries. They will usually ship to just about anywhere in the world, as long as the plants that you are requesting are not blacklisted in your area.

Lemon verbena responds to pruning by producing new leaves at the whorl immediately below the cut rather than along the entire stem. As a result, this shrub can grow leggy. It requires regular pruning throughout the year to increase leaf production. Snip off leggy stems just above a leaf whorl.

They do tend to like warm climates, as the cold will quickly kill them. Also, they like quite a bit of water, but just as any plant, they will contract an infection in oversaturated water.

In the meantime, this article will help you with the care of these: https://www.gardeningknowhow.com/edible/herbs/lemon-verbena/tips-for-growing-lemon-verbena-herb-in-the-garden.htm

The plant looks more like lemon verbena than a tropical cedron tree. The small balls are probably leaf galls, abnormal growths caused by insects, mites, fungi, etc. Control is not necessary as they rarely affect plant health.

The brown edges could indicate lack of water. Be sure you are watering deeply when you water.

The holes may indicate a chewing insect so try a strong stream of water, horticultural soaps or neem oil to eradicate the pest.

https://www.gardeningknowhow.com/edible/herbs/hgen/herb-growing-problems.htm