We have been on winter break and received your question this date.
The browning of the banches looks like it may be old scattered damage. There are several insects and diseases that can impact Leyland cypress, not to mention problems caused by improper planting, root damage and other abiotic problems. Leyland cypress do not recover well from any type of root loss. They grow best in full sun with plenty of air circulation and appreciate moisture during dry periods.
All you can do is prune out dead plant material in the spring. Scratch the branches with your fingernail and look for green tissue. If you see it, the branch is still viable. Keep the trees watered in dry periods and make sure mulch is not thicker than several inches and keep away from the base of the trunks.
The leyland shown in the picture is the entire tree. Since it is all brown and those on either side are entirely green, I assume it is probably that it did not receive sun? Perhaps it might also be roots? If it were insects or disease would that not spread to others? Also, in transmitting the pictures, the trees are on their side. Rotating them 90 degrees will make the picture easier to view.
Once a plant dies, it is impossible to determine the cause. Keep an eye on your other Leylands and notify us immediately if you see symptoms.