Light Emitting Diodes operate at very small voltages and draw little current as you have found out. For RV use, they are configured to operate at 12V but will endure a few volts more.
I'm going to guess that the store you visited had a display that was powered with a 12V power supply. The power supply was probably powered by the standard 120V AC mains power.
Yes, your cigarette socket will offer the 12V necessary to power an LED array (as that is usually how they are built, not a single diode).
BTW, 120V and 12V are not measurements of current. They are measurements of voltage. Current is typically measured in Amps (A) or Watts (W).
