Can it be ascertained by simply reading someone's words on a page or is it necessary to sit across from someone, look him or her in the eyes, and judge by body language and facial expressions/cues?
There are supposed to be telltale signs of lying. Sometimes a person will shift their eyes away from the person they're talking to. (not make eye contact) (Of course that could also indicate shyness.) I think constantly rubbing the nose is another sign. (But then again the person could just have an itchy nose.) A nervous laugh might be another indicator. Moving the arms around might be employed to distract the other person from what is being said. But again, it could just mean the person is nervous.
Some people are easy to read; others are not. When it comes to stories, we don't have the luxury of seeing what someone's characters are doing, so as writers we need to make these characters come alive on the page.
How would you make this person appear to be lying?
Sally looked at John and started telling him her story.
Maybe you can rewrite the above line in the comments box.