Cal admits himself to a mental hospital on the episode "Pied Piper." His goal? To determine the innocence or guilt of a killer.
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This is a scene from the Lie to Me episode "Pied Piper." During it, Lightman is witnessing the execution of a man he helped put away.
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Cal watches an execution in this scene from Lie to Me. The man who is killed is someone he helped put away.
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Lie to Me Season 2 Episode 19 Quotes

Agent Reynolds: Frankly you are beginning to sound a little insane.
Lightman: Really?
Reynolds: Really.
Lightman: I was hoping you would say that.

Eli: Does Lightman seem weird to you?
Tia: He's rude, impatient, distant, seems pretty normal to me.