Disinfect your pruning tools before and after use on an ailing tree to reduce the chances of spreading disease. Soak your tools in a bucket filled with 25 percent bleach solution. Mix this solution by adding 1 part bleach to 3 parts water, and soak the tools for at least five minutes.
Prune a dying Lawson false cypress in late spring or early summer so it has the best chance for new growth during the growing season. These trees are slow to replace growth, and old wood produces no new growth.
Prune off all dead branches of the tree, using pruning shears for smaller limbs and a pruning saw for larger ones. Look for dead, browning branch tips. Follow them back to the trunk, and cut them where the branch meets the trunk. Avoid cutting into the trunk itself, as these wounds are slow to heal. Wear work gloves to protect your hands while pruning.
Remove branches that are crossing one another, as they are likely to produce rubbing wounds over time. These wounds make the Lawson false cypress more susceptible to disease.
Promote new growth using the heading back method of pruning. Remove just a few inches of branch tips in areas where you wish to produce thicker growth. Make these cuts at a branch fork, but do so sparingly, as heavy pruning may cause permanent bare spots in your tree. Only the green, actively growing branch tips will produce new growth. While heading back, you may influence the shape of your tree by choosing to cut either inward or outward growing buds.