Not all sockets are 3-way...it could just be an on-off switch.
Most new lamps have a polarized plug...this puts the hot lead on the middle contact of the socket. Older ones, it's pot luck. If the insulation is worn or the wiring is frayed, or the socket is broken, you could have line voltage on the lamp body. If it isn't an expensive lamp, probably better to chuck it. If you want, you'll probably need to disassemble it and maybe rewire. Don't plug it in until you've checked it out - it could kill you.
If you have a multimeter, you can check to see if you have continuity between either prong of the plug to the body of the lamp...if you do, fix it.