My SO has her been searching for a way to catch me for years. Now she has found an ex FBI man that has a FULL PROOF LIE DETECTOR..... Oh SHIT....
Is she insisting you submit to it? Then refuse to take it -- but also consider taking a long "vacation" and assess what you've done to arouse her suspicions in the first place.
Your grounds for refusal: There is no such thing as a "foolproof" lie detector. As paganguy says, the thing detects nervousness, not lies per se -- the underlying assumption being that liars are nervous when lying. I've read about serial killers who've beaten lie detectors because they have no consciences.
On the flip side -- 20/20 (believe John Stossel) did an expose, at least a decade ago, about employers relying more and more on polygraphs for employee applicant screening and to detect misconduct in the workplace. Setting up a false business (office setting), they brought in one polygrapher after another who was certain of his own/his machine's infallibility; stating that an expensive camera had been stolen (none had), they asked that all their "employees" be questioned, and confided their "suspicion" that "Bob" was the thief. Guess who the polygraphers "fingered" every time as the liar? Were I in your shoes, I'd use this example to argue that of course the ex-FBI agent will find you deceitful.