Hello Tom Thumb! 8))
Everyone one of us have stronger or more dominate side of our body and because we are not perfectly symmetrical, at times we see differences in size when we measure our bodies and compare left and right sides of our body.
Here are some things you can try to increase hypertrophy on the side of the body that is smaller.
1. Use cable machines or dumbbells as opposed to traditional fixed machines. In this way you can really not only increase the strength of the side that is smaller and likely weaker, but you will be able to concentrate on increasing hypertrophy on that muscle group.
2. Ask your personal trainer to perform a one rep max assessment for you for your lats. But perform it unilaterally. In this way your trainer will be in a position to determine the appropriate amount of weight you should be lifting at in order to increase the muscle size of the latissimus dorsi.
Tom, I hope this is helpful to you.