2 wire lamp cord - which one is live?
That's probably an extra-low-voltage DC adapter outputting something like 12V DC.

The word "live" is generally only used for AC 120V or 240V

For low voltage DC the terms are "positive" and "negative". Which is which is sometimes marked on the connector. Alternatively there may be a rib or line marked on one side of the wire. I think that usually marks the positive. If the connector is a typical barrel-plug, they are most often centre-positive - but you can't be sure without testing.

I'd just check with a multimeter to work out polarity. A typical multimeter set to a DC voltage range will show a positive number if the red lead is connected to the positive conductor and a negative number if the red lead is connected to the negative conductor.