1: It's a Bad Moon. Evil omens and restless dead abound. All Chaotic creatures receive a +1 bonus to attack rolls for the duration of the night.
Lawful characters and creatures do not regain HP from rest after a Bad Moon though other sources of healing still apply normally.
2-5: No particular effect. Carry on.
6: It's a Sacred Moon. The crusaders of order push back the horrors of the night.
All Lawful creatures receive a +1 bonus to attack rolls and Chaotic creatures do not regain HP from resting.
In games using 2 part alignment (law/chaos and good/evil) reassign them to Evil and Good or change the titles a little (Moon of Law / Moon of Chaos?)