I also have a brand new machine and had the same problem as the OP. Adding conservative amounts of lubricant does nothing. Instead, I found that slathering on overkill amounts of SuperLube using a glove onto the z-axis lead screws and the z-axis linear bearings instantly cured the problem. When the problem disappears, just wipe off the excess that accumulates near the nuts and bearings, and then you're done.
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RE: Squeaking Z Lift