Actually, it is always full lit. Most people believe all that we see illuminated of the moon from Earth is all the light and heat it gets. In the same vein, most people believe the dark side of the moon is always dark. Also that the moon landings were a hoax. If you have the gear or reserve time online through the major networks of telescopes (all around the globe) you can disprove the notion that the landings were a hoax. You can see the evidence for yourself.
The moon is tidally locked with Earth. Meaning that though the Earth spins once each day, whether you see it or not, the moon does not spin. The same side is always facing us. We see it wax and wane. Whenever there is a “new moon” and none of it is lit up from our perspectives, the “dark side” of the moon is fully lit. This is because, being tidally locked with Earth, the moon itself does not spin. It does orbit the Earth once every 28 days, therefor causing the moon phases we see. The side facing us (as well as the dark side) has one sunrise to sunset span of 14 days. Being that it does not have a strong atmosphere (almost no atmosphere at all, really), wherever the Sun touches the lunar surface, it gets up to 107 degrees celsius (225 degrees fahrenheit) and once the sun sets, it almost immediately drops to -153 celsius (-243 degrees fahrenheit).
Food for thought.
The half moon is the best time to view it as a bulk of the cool craters facing us are illuminated and cast large shadows.