Hopefully you have a digital voltmeter. I would measure the terminals on the switch side of the plug with the switch in the "On" position (out). If you have any resistance, the switch is bad and acting as a heater element. I suspect this is what you'll find, based on your description. If the switch is good, unplug each Lucas light and measure the resistance of them. Both should be about the same. If one is at or close to 0 ohms, the bulb or fixture is shorted. If both are the same, add the two resistance numbers together and divide by 2. Now plug the lights back in and measure from the harness side of the fog light switch plug to ground. Your reading should be close to the number you just came up with. A little higher is ok, because of resistance in the wire. A lot higher means your wire is probably broken somewhere. Lower means the wire is shorted to the metal body somewhere where the insulation is worn off.
Steve