You may want to get evaluated to see what is exactly going on. Then, train each side separately with free weights instead of machines to isolate the muscles individually, as much as possible since the body works together.
No cheating, form is important to let the smaller side catch up to the larger side.
Have fun finding your symmetry; but, do not stress over it, no one is perfectly symmetrical.
I’ve experienced this in the past myself. There is always a chance it’s genetic, or something neurological, or even the exact location of the insertion points of the muscle (back to genetics). In some cases you may need to refer them to a more qualified professional.
But, I’ll tell you what I did, and what helped me with this situation.
I had a strong overly-dominant right lat, and a weak and virtually inactive left lat. Unilateral training is the key to this. The latissimus dorsi is a large powerful muscle that is used in many different movements and exercises.
Keep in mind that MOST lat exercises are going to feature your biceps/elbow flexors as synergists. So, you should also assess wether or not your left and right biceps have any imbalances. I had a strong tight left bicep that was over-active and probably dominating the rowing and pulldown type exercises.
If this is the case, warm up the tight biceps with a couple of sets of curls. And spend a few minutes with more than one type of stretch. Look up Dynamic stretches with palms to the ground, for this. Anyway, stretch the biceps really good, and focus on feeling the lat do its job when you do the rows or pulldowns.
Also….front planks, and especially side planks are awesome for helping strengthen the weaker lat. It doesn’t seem like a big lat move, but trust me on this. Incorporate these into your workouts.
Do some of your lat exercises with lower weights, and a little slower and focus on feeling the contraction of the last rather than moving the weight with all of your might at a heavier weight.
Unilateral/one arm -straight arm pulldowns are also good for this! Standing or lying supine.
Hope this helps!!!!
All good answers. I like seated, unilateral pull-downs using the high pulley on the lat machine. To fully load shoulder adduction and, especially, shoulder girdle depression, I think the seated position on a lat-pull machine is the best. Be sure to use a resistance that takes the target muscles to temporary failure in 8-12 reps.