The Lie Detector works by measuring galvanic response. In other words, when a person lies, they tend to sweat. Perspiration has a high sodium content, so sweat is conductive. Dry skin has a resistance of about 1 million ohms, whereas the resistance of moist skin is reduced by a factor of ten or more.
A person holding the probe wires will change the voltage at the upper probe wire depending on their skin resistance. The skin resistance is in parallel with R2 and, because it is likely to be similar to or smaller than R2, the voltage at the probe wire will fall as skin resistance falls. A 9V battery is required but not included.