"Lie detector" questions should be directly designed to evoke a physical reaction that could be seen in the results.
The answers to questions put forth in a polygraph test (the technical term for a 'lie detector') should be binary. Little in way of explanation should be present. We are looking to see what the machine can find in the reactions of the subject. For example, Abigail should be enlisted in taking a polygraph test. The questions asked of her would delve into her actions. For example, "Did you have sexual relations with John Proctor?" or "Did you lust after John Proctor?" would be the type of questions that could force Abigail to acknowledge her feelings about John. Throughout the play, Abigail's emotional state regarding Proctor is never vetted. If some level of delving had occurred, Abigail's credibility might be questioned. Another question that might generate interesting polygraph results would be to ask Abigail if she went into the woods to conjure a spell against Goody Proctor. Parris begins the process of asking Abigail about that night in the woods, but she does a great job of inverting the dialogue and creating misdirections so Parris relents in his questioning. In a lie detector test, Abigail could not successfully utilize her evasive tactics.
Near the end of Act I, the girls follow Abigail's example and identify "witches" in Salem. The girls are taken at their word. No one questions their claims. As a result, putting them under a polygraph test is entirely appropriate. I would ask Betty when she saw Goody Bibber with the Devil, and I would ask Abigail when she saw Goody Hawkins and Goody Booth with the devil. I would further ask Abigail where she was when she saw Goody Sibber with the devil. I would try to ask direct questions that would force the girls to give specific details that do not exist. I think subjecting the girls to direct and focused questions that would force them into lies would be when the lie detector could be most effective.