It is strange that this is not a universal problem, making the cause of the noise rather mysterious to me. I never had that noise with them using their black cleats, albeit with the rubber piece in the center removed because I don't really see its use. Perhaps that's the reason?
I sure wish I could have solved it. If you read my entire history with these Looks in this thread you can see that I tried a lot of things and got them silenced for brief periods. I liked a lot of things about the pedals. But it seems like a construction tolerances issue. The cartridge bearings are very loosely fitting into the composite body, so unless the grease is heavy and fresh, it starts clicking internally. I think the pedals-to cleat squeaks are a separate issue that could probably be solved with correct choice of lubes.
It is not a universal problem, but browsing the discussion boards it does seem to be a very common problem.
Another aspect is that they were much quieter when easy spinning. It was usually when climbing at about 70 RPM that the noises would drive me nuts. I am not very powerful, so we can't blame it on me putting and unusually high power to the pedals.
By contrast, my Shimanos are all dead-silent with no thought to maintenance at all, even after at least a year, including a winter, of riding. My Speedplays were also silent by comparison, although the did make a very slight click sound when reaching the edges of the float restraint if your foot changed angles while pedaling. But that was understandable as a metal-metal contact that was the intended method of operation.
But IF your Looks are silent, then they are a great pedal. I am envious!