No; all logically, sentimentally and psychologically. By definition (just read a dictionary), a lie requires intent to deceive. Although it's possible that a person might alter their own intent when hey find that someone trusts their sarcasm, normally and initially they will have no intent to actually mislead. They want their sarcasm to be detected; their goal is to mock, not to mislead. . Fun fact for ya: sarcasm is hypothetical mocking (ex. "Let's just do everything we can to fail,") sardonicism is literal mocking (ex. "Yeah, you go ahead and do that.")
No, although it can be used as a form of equivocation.
A politician, faced with a difficult question, may reply sarcastically to divert the questioner (whether a rival politician, a journalist, or a constituent) and, in doing so, hasn't told a direct lie but has avoided the truth.
In fact, when a politician is asked a question that can be answered Yes or No, if he says ANYTHING else, he is probably equivocating or obfuscating. If you don't know the words look them up. They're a necessary tool for understanding the way our politicians lie.