Besides this species being called the cadillac of Zoysia, it has limits. It is subject to leaf spot, dollar spot, brown patch and thatch is overfertilized. It is a slow grower and has low growing habits. As far as growing back in after damage, it is best to resod those areas rather than plugging them. With 4 inch recovery growth in a season, that is all you may get for speed. Golf courses here are using it in the fairways and in adjacent homes built on the course. Lower maintenance is required with the areas of over all cost. Repairs to damaged zoysia is always dealt with by replacement pieces and not plugs.
There is no way to detect what may have happened to this clients lawn. Dead spots can be winter injury, misused herbicides to control crabgrass, lack of water during last seasons droughts, and or improper installation or wrong site placement.
If this customer isn't wanting to repair the damage, then be assured there will be weed out breaks and all you can do it is mow as usual.