Troubleshooting Clamp Meter
You say that you put the clamp around a live lamp cord, but for a clamp meter to work, you have to put the clamp around only ONE of the conductors.  If you clamp around both wires, you will not get a reading.  For most situations, it doesn't matter which single wire you clamp around.

They have devices that you can plug in that give you holes to put the clamp meter:



Image source: Line splitter at Home Depot website

The one pictured also has a hole for a "10x" measurement.  It just has 10 loops of the single wire in it so measurements taken there will be 10 times higher (good for getting more precise measurements with a less precise meter).

Or you could make one with some single conductor wire and a male and female plug.