If Chris Christie lied, he did so under oath. Bill Clinton was impeached for a similar offense, and it would mean that he had the opportunity to defend himself at a trial. He has a right and a duty to stand trial for the crimes he commited while in office.
Governor Chris Christie should be impeached if it is discovered he lied regarding the Bridgegate scandal. This wold prove he was at least part of the cover-up, and perhaps even involved with the decision to close lanes. As President Nixon once said regarding Watergate, the cover-up as worse than the crime.
If Chris Christie lied about Bridge-gate, then yes, he should be impeached. Christie has claimed to have not known anything about the scandal; even firing a staff member that was discovered to be involved. However, Christie is not above the law, and should be held accountable if found guilty. He does have just a year left in office, so he will probably not be impeached.
Impeached? He should be prosecuted. It is theft to abuse one's authority as a public servant to use a public good for your own benefit. Christie stole the use of the bridge, worth millions, for the benefit of his own campaign. He owes the residents of Fort Lee a lot of money in damages for their days in traffic.