Can't explain

Digital meters depending on the type are notorious for low voltage readings that are false. Try turning the meter on and letting the probes be in free air. Take a reading, now wave them about..
Try an RMS meter if you have one.

Sure, the frame of the lamp is connected to the wide blade of the plug and that
connects the frame to the neutral conductor in the outlet. Depending on the other loads on the same branch circuit that the outlet is on there will be up to several volts dropped (I * R) along the neutral conductor back to your main panel where neutral and ground are connected together. Since ground conductors USUALLY do not have any current flowing through them, the voltage drop across them will be essentially zero. Using a water pipe
as your ground reference will probably give you the same indication. ........ On second thought, and after reading your post again, the wide blade of your lamp plug should not be connected to the lamp frame. Unplug the lamp and measure the resistance of each blade to the lamp frame with the switch on and off. In both cases the resistance to the frame should be very high. If not, find the short, and fix it.
ARM

"False" is not the word I'd choose. DMMs have a very high input impedance - as a result, even a few picofarads of capacitance between the power circuit and the lamp frame could provide a high impedance that would allow this reading to appear on the meter. 120 V / 2 V = 60, typical DMM input is 10 meg ohms, and 600 megohms is the impedance of about 4.5 picofarads at 60 Hz.
In my old steelmaking days we had a mimic panel for a dust collector that was quite hard to read - it used neon lamps to indicate damper positions, and since the lamps were connected to a couple hundred metres of cable, it was very easy for stray capacitance to provide enough voltage to allow the neons to light.
RMS isn't so much the problem as the high impedance. If you're looking for hazardous leakage current, use a low-impedance tester (a Wiggy or Square D) or a purpose-built leakage current test set.
Bill

Incorrect measurement technique. Put a load - like a 100 watt bulb - across the meter leads, then take your measurements. A digital meter doesn't put enough load on branch circuit wiring to avoid erroneous low voltage readings.

The static voltage or minute power is either capacitively coupled or induced from conductor to frame. The power should be canceled in theory, with the zip cord conductors direction of current being 180 degrees out of phase. Perhaps one of the conductors is longer at the beak-out point or one conductor is closer to the frame. Either way, it would appear to involve asymmetry.

"static voltage" Sorry, not the case unless measuring in D.C.

It is all relative. One of the conductors is usually tied to ground. If you measure voltage relative to ground, the induced voltage, due mainly to capacitive coupling from each conductor, is somewhere between the hot and ground. John