Lying on control questions is not advisable. A polygraph would be conducted inside of a larger investigation which would, among other things, fact-check your claims by other means. These data would be considered in the interpretation of your polygraph results. Whether or not you live in Chicago is very easy to check; when they see that you are lying on control questions they will consider everything else suspect.

In the contexts in which polygraphs are applied (i.e. security clearance, witch hunts within security services), simply being suspicious in this way is enough to cause the negative outcome (i.e. not getting the clearance, getting fired), so even if it might muddy the evaluation of your response to, i.e. "Are you a Russian spy?" it would still cause the negative outcome.

It has no bearing on criminal prosecution, because polygraphs are already inadmissible.