Can you grow Lawson cypress in zone 4?

No, it may not be a good idea to grow Lawson cypress [Chamaecyparis lawsoniana] in zone 4. The tree prefers zones 5B-7. It's picky about sitting in moist but well drained, non clayey soil; receiving full sun; benefiting from more humid environments; and being protected from constant or harsh winds. It's a beautiful tree. But it really likes the conditions within its native, North American range in Oregon and California.