Identifying the hot and neutral wires of an antique lamp
I assume the lamp has a screw socket for the bulb. In this case, the hot wire connects to the contact at the bottom of the socket and the neutral connects to the screw shell.
You may be able to examine the socket to see which connects where. Otherwise, you’ll need a way to determine electrical continuity (ohm meter, continuity tester, battery and flashlight bulb, etc.) to determine which wire connects to the bottom and is therefore hot.