There are several themes in Polygraph by Lepage and Brassard. Two that come immediately to mind are: the difference between reality and perception, and that things are not always as they appear.
Reality often is the root cause of unhappiness in one's life. Francois and his boyfriend have a fight: we can infer that the crying David hears through Lucie's apartment wall may be caused by trouble in Francois' personal life. However, we find that Francois is also tormented by his past—the time when he was suspected for Marie's murder. David tells Lucie that the police purposely do not reveal the results of the polygraph test. David explains that the "fear and mystique" of the test can be intimidating, sometimes bringing about a confession. But he also notes that the process can be damaging, and he warns:
But such strategies, I believe, should be used only with great care and compassion. Sometimes, the psychological response we trigger is so violent as to effect a lasting disorder in the mind of a totally innocent suspect.
Francois, it appears, is one of these innocent people. His perception is that he is still a suspect, and this thought haunts him.
David reports to Lucie that the intimidation of that interview has never ended:
...the police never told [Francois] he was released from suspicion...He was never let off the hook.
When David asks questions of Francois when he is moving out of his apartment, Francois becomes defensive, showing that he is still tormented:
Why do you ask me so many questions? You sound like an interrogator...
Lucie directly asks Francois if he killed Marie. Francois is so damaged by the experience that he is no longer sure—a statement allows us to infer that he believes he is innocent—but in living with perceived suspicion for six years, he can no longer be certain.
I don't think [I killed her]...I don't know anymore.
The second theme of note is that things are not always as they appear. This is introduced when Lucie tells David that actors use a substance to induce fake tears when they cannot make themselves cry on their own. David notes that this practice is dishonest:
What a deception! I believed that for an actor at least, tears were the ultimate proof of emotion!
When David tries the drops, it is interesting that he cries while he thinks of leaving Anna behind in Berlin, but we sense it was his choice to leave and never return. While Anna's letters expresses regret, we don't get much emotion from David anywhere throughout the play except when he learns that Lucie has slept with Francois because she felt badly for how unhappy he is. Even then, David masks his emotions and Lucie chides him for it.
The idea of "deception" is also introduced when David gives Lucie the gift of the Russian "Matruska" doll. Also known as nesting dolls, the largest doll opens to reveal a smaller set of dolls inside, each smaller and hidden within a larger doll. Of the hidden dolls, David says:
...I like to think it may stand for other things like...Hidden feelings...One truth which is hiding another truth and another one and another one...
David is not concerned with exposing the truth, (as seen with Francois) but in hiding it. When he tells Lucie about the polygraph, he makes her promise to say nothing to Francois. He also hides his own feelings, seeming to have no concern for anyone: not for Anna, or even Lucie after she sees the suicide. David keeps truths hidden.