No, there's a crossed wire, probably in the socket where the wires are screwed in.
Unplug the lamp. If you have to, turn off the circuit breaker. Check the lamp cord. Do you have a pet or child that could have chewed on the cord and crossed the wires?
Check the plug itself to see what condition it's in.
But, usually, the problem is in the socket wiring. You can screw off the socket from the base. On some of them, you can simply pull off the socket sleeve. Check the wires at the screws. If one looks frayed, loose and is poking out and touch other metal, instead of being tucked directly under the screw, take a screw driver and push it back under the screw.
If you don't see any frayed wiring, the socket may simply need replacing. That's pretty easy to do also. It's only $2 for a new socket at Home Depot. You can even change to a 3-way light bulb socket if you wish. Directions are on line some where to install the new socket. Takes all of 5 minutes. Google for them.
