Maybe he is lying, maybe not. Anyway - look at running around you do not specify. A common belief is that the liar's eyes run - a myth that has recently been completely refuted.
Psychologist Richard Wiseman conducted two experiments. One group of participants to lie, he asked that they put cell phone in a drawer, while in fact lay the phone in their pocket. The second half of the phone asked to put in a box and tell the truth. Wiseman then analyzed the video of people's behavior. In the second experiment, he watched the recording of actual cases of proven false testimony in the police and the courts.
And in the first and in the second case observe any connection between the "downhill" look and vranёm failed. Nor it was observed that liars often look to any preferred side: right or left.