I have to agree, concluding that theater is "lying" is asinine. Acting may be a form of deception but not all deception equates to lying. Deception is a component of lying however deception in and of itself does not equate to lying just as brick in and of itself is not magically its own house.
In order to "lie" you need to have the intent to deceive. In theater, the audience is a "willing" member that already knows upfront that they are attending a performance. Thus, it is impossible for theater to be "lying" simply on the basis that the performers are pretending to be characters...
Now, if the theater said, "Tom Cruise will be playing the role of Romeo" and then Tom Cruise does not play that role. Then that is lying. But Tom Cruise playing Romeo is not lying, it is performing...