Limit watering if there is regular irrigation. Lawson cypress can handle weeks without supplemental watering. If the weather is very hot or windy, however, insert your finger into the soil. If it feels dry several inches down, water from a hose slowly and deeply. Let the water soak deep into the ground so the roots need to reach for it. Shallow watering can cause root diseases.
Spread 2 to 4 inches of mulch around the base of the tree. Keep it 2 inches from the trunk itself. The mulch will keep the soil moist during the hot stretches.
Prune diseased, weak or dead branches as you notice them. Cut them off where they meet healthy wood. Prune specific branches to control the size of the tree. Lawson cypress gets very large, unless you planted a dwarf version. Shear new growth to shape the tree.
Protect the tree from winter injury. It can dry out in the cold temperatures, so continue watering it during long dry spells, even in the winter.