My calculations based on .25 Lux measured from Earth and using the inverse square law resulted in around 12,000 Lux for lunar surface brightness. NASAs theoretical brightness is 5,500 Lux. Unfortunately there are no published, measured values of lunar surface illumination levels over the course of a lunar day. The only measured values I can find are from the Apollo 8 mission when they used the 2 degree spot meter on the sun lit portion of the far side and recorded between 160 and 320 Lumens. I think that means that the far side is actually quite dark.